[11] Terry Clawson played at second-row and scored four goals in Bradford Northern's 17–8 victory over Hunslet in the 1965–66 Yorkshire Cup Final during the 1965–66 season at Headingley, Leeds on Saturday 16 October 1965.
In October 1968, Hull Kingston Rovers signed Clawson in an exchange deal which saw Geoff Wriglesworth and Frank Foster join Bradford Northern.
A week later, he played and scored three conversions in Leeds 9–5 victory over St Helens in the Championship Final during the 1971–72 season at Station Road, Swinton on Saturday 20 May 1972, and was awarded the Harry Sunderland Trophy for his man of the match performance.
Clawson played at prop (replaced by interchange/substitute Tony Fisher) and scored 5-goals in Leeds' 36–9 victory over Dewsbury in the 1972–73 Yorkshire Cup Final during the 1972–73 season at Odsal Stadium, Bradford on Saturday 7 October 1972, and played at prop in the 7–2 victory over Wakefield Trinity in the 1973–74 Yorkshire Cup Final during the 1973–74 season at Headingley, Leeds on Saturday 20 October 1973.
Clawson played at prop and scored two goals in Leeds' 12–7 victory over Salford in the 1972–73 Player's No.6 Trophy Final during the 1972–73 season at Fartown Ground, Huddersfield on Saturday 24 March 1973.