1918: Saint Clare Mission Church on Giffords Lane
1920: Church cornerstone ceremony on Nelson Avenue
1921: Saint Clare Church in The American Architect journal
1927/1921: Rectory and old Church in original position
1936: Original appearance of Saint Clare School
c.1955: aerial view of Saint Clare neighborhood
1957: preparing to move the old Saint Clare Church
1959: architectural lineage of the new Saint Clare Church
1959/1969: stained glass windows of the Life of Clare
1959/2002: Möller/Peragallo pipe organ
1963: award-winning Saint Clare Presentation Convent
1979/2001: 16' Clare statue / award-winning Pre-Kindergarten
2002: Eternal Flame honoring World Trade Center victims
2003: constructing Faith Formation Center under Chapel
TODAY: Church property map and satellite view

(Click online images or underlined links for more detail.)

1918:
Staten Island's first Catholic church was established in 1839,  Saint Peter Church in New Brighton. Before then, priests occasionally ferried over to lead services at the  "Holy Spring House", a small private home that stood along Giffords Lane at Dewey Avenue for about two centuries until a 1975 fire. Starting in 1862, mid-Island Catholics could travel by foot or horse (or eventually by trolley) to receive the Sacraments regularly at  Saint Patrick Church, which became one of Richmondtown's historic landmarks.

Finally in 1918, Saint Patrick's new pastor, Father Charles J. Parks, established the Mission Church of  Saint Clare of Assisi in a rented hall at 105 Giffords Lane, near Katan Avenue. This frame building was modest in size and appearance, but proved to be quite a versatile asset for the residents of Great Kills. It served as Saint Clare's temporary church until 1921, then as the Mission Hall and Parish Hall until 1953, and next as an American Legion post until 1985, graciously hosting the start-up years of Saint Clare's Pre-Kindergarten during 1977-1979. The building was ultimately replaced by private homes in 1987. This blurry photo is from the neighborhood's Memorial Day parade in 1961.
1920:
On May 19, 1920, Archbishop Hayes ceremonially laid the cornerstone for Saint Clare Church (today's Chapel) at the hilltop of Nelson Avenue. This black-and-white snapshot, and a few similar ones from the same occasion, are (so far) Saint Clare's only known photos before the school's first graduating class in 1938.
1921:
The new building was said to be the first Catholic church in the United States designed in simple Colonial style, rather than traditional European form. As construction finished in 1921, the young architects,  Otto R. Eggers and parishioner Daniel P. Higgins, were featured in  an article of The American Architect for their patriotic innovation. In later decades, they went on to design the original portion of Saint Clare School (1936) and many prominent American buildings.
1927/1921:
This vintage postcard shows Saint Clare's Rectory (1927) next to the old Church (1921), in their original position along Nelson Avenue. The 2.5-story rectory, containing living quarters and the parish office, harmonized with the residential neighborhood, and maintains essentially the same appearance today. All the exteriors of Saint Clare's later buildings would match in red brick.
1936:
The original Higgins-designed Saint Clare School opened on September 14, 1936, at 151 Lindenwood Road, modestly sized for the Great Depression. The building was more-than-doubled with additional wings in 1959 and 1990, as the neighborhood grew and prospered. Parish artist Louis Padavano prepared this detailed drawing of how the school would have looked in 1936 when it was new.
c.1955:
A brave photographer's flight over Great Kills gave us this aerial view of Nelson Avenue (top of the photo below) and Saint Clare's in the 1950s: church, rectory, and school. The old church had not yet been moved to its new location as today's Chapel. Construction had not yet begun on the new church and the expanded school. Near the bottom of the photo, the house just south of the school on Lindenwood Road had not yet become Saint Clare's Presentation Convent. Within the next decade, all these plans would come to fruition as the  Verrazzano Bridge was built and the parish tripled in population.
1957:
In October 1957, the old church was physically moved to allow space for the new church's foundation. The  YouTube captions are not quite right -- the church building that moved was Saint Clare's second (1921), not original (1918), and the auditorium was not moved. Still, thanks to Denis "Bob" Fleming, the longtime property supervisor, these old film-clips give a wonderful glimpse of parishioners preparing to roll the old church 100 yards down Nelson Avenue, to the site where it stands as today's Chapel, still in daily use.
1959:
Saint Clare's 1959 church combined both a modern flair and a distinguished architectural lineage, thanks to its architect  Joseph Sanford Shanley, a leading specialist for Catholic churches on the East Coast. As a fine example of adaptive design progression, Saint Clare's octagon-shaped, red-brick exterior in Colonial Revival style was patterned after Shanley's earlier Church of Saint Charles Borromeo (Newark 1937), which  The New York Times hailed as "outstanding." Saint Clare's open, brightly domed interior drew inspiration from the first Catholic cathedral built in the United States. Baltimore's Cathedral of the Assumption was consecrated in 1876 by one of Shanley's prominent relatives (Archbishop James Roosevelt Bayley) and was prestigiously declared a Basilica in 1937. Saint Elizabeth Ann Bayley Seton, the family's Catholic founder whose vocation led her from New York to Baltimore, was the archbishop's aunt and the architect's great-great-great-aunt. Shanley designed her Shrine Church as his final project, at the former site of her Manhattan home by the Staten Island Ferry. Shanley connected Saint Clare's new church and the expanded school by two indoor passageways, and architects  Belfatto & Pavarini further expanded the school in 1990. The church in 1959 was the first on Staten Island to have central air-conditioning, and now the school is fully air-conditioned as well.

1959/1969:
Fund-raising for Saint Clare's 1959 expansion project surpassed $1 million (more than $10 million in 2021 equivalents). As a result, the new church was able to include nine prayerful stained-glass windows depicting the Life of Clare in 13th-century Italy, by Staten Island artist Michael A. Zappalorti Sr. The intricate installation was completed in 1969, and the parish published a  glossy booklet describing the windows in 1994, to honor their 25th year and the 800th anniversary of Clare's birth. The interior church walls were sky-blue at the time, matching much of the school and the old church (today's Chapel). Window scenes, counter-clockwise from the altar:
1. Clare joins Francis and receives habit and short haircut, 1212
2. Clare invokes the Eucharist to defend against first army, 1240
3. Clare receives guidance from Francis, ~1210
4. Clare humbly washes the Sister's feet, ~1220
5. Clare meets the visiting Pope Gregory IX, 1228 (shown above)
6. Clare mourns the death of Francis, 1226
7. Clare invokes the Eucharist to defend against second army, 1241
8. Clare dines with Francis, to the glory of God, ~1223
9. Clare, future Agnes, and cousin Rufino encounter Francis, 1212

1959/2002:
The 1959 church was also able to include a modest pipe organ from  M.P. Möller, Inc., with the console and enclosed pipes to the right of the altar, and exposed geometric pipework in the rear gallery. The instrument was later expanded in 2002 by  Peragallo Pipe Organ Company and  Schulmerich Bells, at the initiative of Saint Clare music director Daniel R. Palko and an anonymous bequest.
1963:
In November 1961, Saint Clare Parish purchased the red-brick house next to the School along Lindenwood Road, for the faculty of  Presentation Sisters who had been commuting every day since 1936. Parishioner Kenneth W. Milnes designed the conversion and expansion of the 1931 house into a sixteen-room Convent with its own chapel. By September 1963, construction was complete, the rooms were furnished by parishioners, and twelve Presentation Sisters moved in for the start of the school year. The Chamber of Commerce bestowed an architectural award to Saint Clare's Presentation Convent soon after, proclaiming it one of the best building projects completed on Staten Island that year. In 1999 it was  re-dedicated as the Presentation Center, providing much-needed office space and meeting rooms for the many lay ministers carrying forth the retired Sisters' legacy of service to Saint Clare parishioners.
1979/2001:
The main Nelson Avenue entrance to the parish's Cardinal Cooke Center (1979) features a contemporary 16-foot statue of Saint Clare, one of her largest in the world, sculpted by longtime parishioner  Hans Karl. (A 20-foot statue may be the only larger one in the Americas, built by a California sculptor in 1965 for the saint's namesake city of Santa Clara.) The classically styled 4-foot Clare statue above the main entrance of our 1959 church was another Karl creation. Saint Clare's Cooke Center was designed before the parish had a Pre-Kindergarten program, which soon began using most of the upstairs space. (Downstairs is a heavily used gym.) A major 2001 renovation of the Pre-Kindergarten area earned an  Honor Award from the American Institute of Architects, for the playfully modern colors and shapes designed by parishioner David L. Businelli and professor Stephen Perrella. Their design received national attention in early 2003 when it was featured as  the cover story of Contract magazine.
2002:
Next to the outdoor Shrine of Our Lady of Fatima and the Pathway of Prayer is a poignant tribute to victims of the  World Trade Center attacks of September 11, 2001. This Eternal Flame memorial was commissioned by Saint Clare Parish and its extensive  WTC Outreach program, with substantial contributions from the KeySpan gas company (formerly Brooklyn Union Gas, now National Grid). The lamp, pedestal and plantings are prayerfully simple, and the ground-level red bricks name and honor the  29 parishioners who died suddenly from the tragedy, including 11 firefighters and a stillborn baby. The dedication on September 6, 2002, was attended by 600 people and was featured on the New York television news. The designer was parishioner David Businelli, who previously won architectural awards for Saint Clare's landscaped Pathway of Prayer (Chamber of Commerce, 2000) and the innovative Pre-Kindergarten (Chamber of Commerce, 2001; American Institute of Architects, 2002).
2003:
The foundation of Saint Clare Chapel (the wooden church building from 1921, relocated in 1957) gradually deteriorated from ground settlement, heavy vehicles in the parking lot, water seepage, dry rot, and hidden termites. By the time the extent of the damage was discovered, the historic and beloved Chapel was nearly lost. Instead, the parish committed to the extensive reconstruction necessary, received generous 9/11-related grant funding, and took the opportunity to convert the sunken crawl space into a finished basement, as another Businelli project. This large and flexible meeting space (including a lending library) was designated the Faith Formation Center, and the "before and after" photos testify to the magnitude of the underground task. With suitable care and maintenance, the above-ground Chapel will gracefully serve its second century of hosting daily Masses and Eucharistic Adoration for Saint Clare parishioners.
TODAY:
After decades of heavy growth, Saint Clare's now has six principal buildings dating from 1921 to 1979: the church, school, converted convent, parish center, chapel, and rectory. In counter-clockwise order, they surround the perpetually busy central parking lot, and in turn are surrounded by the suburban neighborhood's detached one- and two-family homes. The church property occupies 2.5 acres between Lindenwood Road and Nelson Avenue, within the long block to the north of Edgewood Road in the heart of Great Kills. -----------------
Most of these Architectural Highlights were summarized and illustrated by Gregg Patruno in 2018-2019, under the supervision of Monsignor Richard Guastella. The information was assembled from parish archives, "History of Saint Clare Parish," and other reference sources. Further suggestions are welcome.

See also:
" St. Clare's Church (Staten Island)," from Wikipedia.