Terrance Sheahan attended CBHS Lewisham before studying at the University of Sydney, receiving a Bachelor of Arts and a Bachelor of Law in 1969. He worked as a solicitor from 1967 and was called to the bar in 1982. He joined the Willoughby branch of the Labor Party in 1964 and went on to be a member of the Yass, Cootamundra and Gladesville branches.
In 1973, Sheahan was elected to the NSW seat of Burrinjuck. He was secretary of the Parliamentary Labor Party from 1976 until his elevation to the ministry in 1980. Over seven years, he served as Minister for Housing and Cooperative Services, Energy and Finance Minister, Planning and Environment Minister, Attorney-General, and Transport Minister.
From 1989 to 1997, Sheahan was also the President of the New South Wales Labor Party. He only resigned to accept an appointment as a Judge of the Land and Environment Court of New South Wales from which he retired in 2019.
Sheahan was awarded the Officer of the Order of Australia (AO) for services to the Law, the Parliament and the Community (health, care of the aged, human rights and the environment).