Contest jam being very thin (10)
I believe the answer is:
matchstick
'very thin' is the definition.
(I've seen this before)
'contest jam' is the wordplay.
'contest' becomes 'match' (match is a kind of contest).
'jam' becomes 'stick' (jam can mean to get stuck).
'match'+'stick'='MATCHSTICK'
'being' acts as a link.
(Other definitions for matchstick that I've seen before include "sort of model" , "Very thin, like figures in Lowry paintings" , "(Of a figure) drawn using thin straight lines" , "Childishly pictured man" , "Wooden part of lighter" .)