Grieve played for Kelso.[2]
He played for South of Scotland District against North of Scotland District on 21 November 1936.[3]
He was due to play for the South of Scotland District against the combined North of Scotland side on 20 November 1937 but he had to withdraw due to an ankle injury.[4]
He played for the Scotland Possibles side against the Scotland Probables side in the final trial match of the 1937-38 season to determine international selection. He impressed the selectors in the first half and then turned out for the Probables in the second half.[5]
He was capped seven times for Scotland, between 1935 and 1936.[6]
Although not Kelso's first Scotland international, when Grieve was first capped in 1935 along with his teammate Gordon Cottington, this was the first time that Kelso provided 2 players in the same Scotland squad.[7]
After his playing career ended he became a selector for the South of Scotland District. He was deemed one of the 'big five' South selectors: along with A. Bowie (Hawick), J. D. H. Hastie (Melrose), T. Henderson (Selkirk) and G. Wood (Gala).[8]
He also was a selector for Kelso.[9]