Gallimore played left-back in the Preston side that won promotion to the First Division in the 1933-34 season. Over the next couple of seasons he spent most of his time in the reserves. However, in the early part of 1936-37 season he played several games alongside his more talented brother, Frank Gallimore.
Preston North End took part in the 1941 Football League War Cup. Preston beat Bury, Bolton, Tranmere, Manchester City and Newcastle to reach the final. The Preston team that faced Arsenal at Wembley on 31st May was: Jack Fairbrother, Leonard Gallimore, William Scott, Bill Shankly, Tom Smith, Andrew Beattie, Tom Finney, Andrew McLaren, Jimmy Dougal, Robert Beattie and Hugh O'Donnell.
The game took place in front of a 60,000 crowd. Arsenal was awarded a penalty after only three minutes but Leslie Compton hit the foot of the post with the spot kick. Soon afterwards Andrew McLaren scored from a pass from Tom Finney. Preston dominated the rest of the match but Dennis Compton managed to get the equaliser just before the end of full-time.
The replay took place at Ewood Park, the ground of Blackburn Rovers. The first goal was as a result of a move that included Tom Finney and Jimmy Dougal before Robert Beattie put the ball in the net. Len Gallimore put through his own goal but from the next attack, Beattie scored again. It was the final goal of the game and Preston ended up the winners of the cup.
Gallimore joined Liverpool but failed to make the first team and moved onto Watford. He played in 64 games for the club but was sacked in 1946. According to Dean Hayes (Who's Who of Preston North End) Gallimore "was convicted several times of criminal offences and twice jailed" while still living in Watford.