A Scottish junior international defender, Andy Clark began his career with Hamilton Academicals and then spent some time with Buckhaven United before getting an opportunity with Hearts in August 1899. He made his debut for the Edinburgh club against Rangers on 2 September but had some disciplinary problems and moved on in May 1901. He came south of the border to join Stoke of the English First Division.

Clark was with the Potters for two seasons, making 52 league appearances, before leaving for Plymouth Argyle in 1903.

In May 1906, he was recruited by Leeds City, and went straight into the first-team, forming a defensive partnership with another Scot, David Murray. He missed just one game until December, but then lost his place to Jimmy Freeborough.

Clark returned to the side on 2 February, playing in a 1-1 draw with Blackpool. Flaneur in the Leeds Mercury: 'This equalising goal was perhaps a fortunate score from the fact that Andrew Clark, who was playing at left-back for Leeds after a long course with the reserves, slipped on the frozen ground when endeavouring to tackle Copestake, and gave the Blackpool right wing a clear course. The ball was centred well, and Dunkley put it through with a very cool shot.'

Clark remained in the side thereafter but left the club at the end of the campaign, having made 24 league appearances.

After departing Elland Road, he returned to Plymouth and later had spells with Brentford and Southend.