Terence (Terry) James Cavanagh was born in Edmonton in 1926. He first ran for municipal office in 1968, but did not win a seat as an Alderman. He ran again in 1971, this time winning a seat, and was re-elected as an Alderman in 1974. When William Hawrelak died in office in 1975, Terry Cavanagh was chosen by City Council to serve as Mayor until the 1977 election. Although he ran for Mayor in 1977, he lost to Cec Purves.
Terry Cavanagh ran again for Council several years later, winning a seat in 1983 and again in 1986. When Mayor Laurence Decore stepped down to run for the Alberta Liberal Party, Cavanagh was selected by Council to serve as Mayor, but was defeated by Jan Reimer in the 1989 election.
Cavanagh was elected to Council again in 1992, and was re-elected in 1995, 1998, 2001, and 2004. He retired from municipal politics after deciding not to run in the 2007 election.