Sekolah Rendah Kebangsaan (SRK) Temenggong Abdul Rahman is from Bukit Zaharah School or the name before independence is Bukit Zaharah Day School. Bukit Zaharah School was opened in 1910 by boarding at the Bukit Zaharah Religious School building which is located near the field of Istana Besar Johor.
In 1956 a school building was erected on Jalan Abdul Rahman Andak in September 1957. The building was named Temenggong Abdul Rahman School Standard Type Primary (English). All students from Sekolah Bukit Zaharah have been transferred to a new school. The school was inaugurated by the Sultan of Johor on 10 October 1957. To assist the administration of the school, the Board of School Managers was formed in 1959 by appointing a former student Tuan Hj. Abdul Karim bin Hitam as the Chairman of the Governing Body.
The number of students continued to increase from year to year until the Temenggong Abdul Rahman branch school had to be opened by staying in an empty building in 1974. The building was SRK (Female) Abdul Rahman Andak or Abdul Rahman Andak National Primary Girls School. Pupils in the branch are female only.
In 1981, the main building of SRK Temenggong Abdul Rahman was able to accommodate all its students and the branch school was taken over by the Armed Forces branch which later became Ngee Heng School in 1985. STAR (1) and STAR (2) were established in 1981.
In 1966, the construction of a new 4-storey building with 2 blocks caused STAR (1) and STAR (2) to be separated. On 27 January 1997, STAR (1) used the old building and STAR (2) used the new building. However, STAR (1) and STAR (2) still share the field.
Sekolah Kebangsaan Temenggong Abdul Rahman (1) (the name of the school from 1 January 1997) got its name from one of the Temenggong Johor who made many reforms and devotion during the 18th century Sultanate of Johor. Temenggong Abdul Rahman is the son of Daeng Kecil Tun Ibrahim. Temenggong Abdul Rahman as the Sultan of Johor, his son Temenggong Ibrahim, his grandson Sultan Abu Bakar (19th Sultan of Johor) and his grandson Sultan Ibrahim then Sultan Ibrahim then Sultan Ismail and now Sultan Iskandar.