Grieve became a journalist, working for the Daily Express and writing the "Voice of Scotland" column for the Glasgow Herald, and later also serving as Arts Editor for Scottish Television .[1] He edited some of his father's work, including a complete anthology of his work, and also worked on a biography of MacDiarmid.[1]
Grieve followed his father into nationalist politics, joining the Scottish National Party (SNP), for which he was elected as Vice Chairman with responsibility for publicity[1] in 1969, serving alongside Hugh MacDonald. Grieve's particular focus was to campaign, but the division of labour did not work well, with Douglas Crawford also involved as Director of Communications, and Grieve resigned in 1972.[3] Grieve also stood unsuccessfully for the party in Glasgow Govan at the 1970 general election, and in Rutherglen in 1979.[4][5]
For the last ten years of his life, Grieve underwent treatment for throat cancer which ultimately led to his death in 1995.[2]