Muir started his career with Lochgelly Violet, the same club that Billy Liddell came from. Winger Muir signed for Liverpool in July 1947 when he was 23 years old. Muir, who had worked in Caldwell’s Paper Mill alongside playing for Violet, had to wait until February 1948 to make his debut as Liverpool defended their league crown they had won in such dramatic style. Muir played four times in the league, games which resulted in three defeats and just a single victory, at Blackburn on 10 April 1948.