On Ron Barassi's retirement, Groom was invited by Melbourne coach Norm Smith to wear the club's prized Number 31 guernsey.
His 1975 election result was significant in that as a Liberal candidate he outpolled a Labor opponent on the West Coast of Tasmania, the first time this had ever occurred.
Groom and his family moved from Burnie to Hobart at the end of 1984 and he was then appointed senior advisor to the Tasmanian Premier Robin Gray.
In 1986 he re-entered politics as a member for Denison in the Tasmanian House of Assembly, topping the poll in that electorate.
In 1991, he successfully challenged Gray's leadership and became Tasmanian state leader of the Liberal Party.
[3] Groom became Premier of Tasmania after leading the Liberals to victory in the 1992 state election with a majority of 19 seats on a swing of over seven percent.
The balance of power rested with the Australian Greens, but the Labor Party refused to enter into any agreement with them.
[5] In the 2010 Australia Day Honours, Groom was appointed an Officer (AO) of the Order of Australia "For service to the Parliament of Tasmania as Premier and through a range of portfolio responsibilities, and to the community through leadership roles within organisations supporting Indigenous, aged and welfare groups".