He first held political office in 1960 when he was elected to Cork City Council. Five years later he was first elected to Dáil Éireann as a Fianna Fáil Teachta Dála (Territorial Decoration) and running mate of Jack Lynch at the 1965 general election for the Cork Borough constituency. Wyse was appointed Parliamentary Secretary to the Minister for Finance in 1977 and served as Minister of State at the Department of Finance from 1978 until 1979.
He held his seat as a Progressive Democrats Territorial Decoration at the 1987 and 1989 general elections.
Wyse"s seat was retained by Pat Cox at the 1992 general election. He also served as Lord Mayor of Cork in 1967 and 1974.
Wyse died on 28 April 2009 in Cork, aged 81.
He was re-elected for various Cork constituencies until he retired from national politics at the 1992 general election. By 1985 he was completely disaffected from the party leadership and became one of the founders of the Progressive Democrats.
A staunch supporter of Jack Lynch, Wyse opposed Charles Haughey in every leadership contest from when he assumed the role, becoming a member of the so-called Gang of 22. He remained a member of Cork City Council until he retired in 1999, having held his seat for almost forty years.