A local junior, he played for Newtown in the 1930s. Stevenson played for City in the hooking role in 1933.[3] He won a premiership with Newtown later that year when he played hooker in the 1933 Grand Final.
Stevenson played in the grand final as a replacement for Arthur Folwell, who had since departed on the 1933-34 Kangaroo tour. Stevenson retired after the conclusion of the 1935 NSWRFL season.[4] Clarrie Stevenson died in Sydney on 28 May 1984 aged 73.[5]