Runner, say, allowed in running heat (7)
I believe the answer is:
athlete
'runner say' is the definition.
(runner is a kind of athlete)
'allowed in running heat' is the wordplay.
'allowed' becomes 'let' (I've seen this before).
'in' is an insertion indicator.
'running' indicates anagramming the letters.
'heat' is an anagram of 'athe'.
'let' placed into 'athe' is 'ATHLETE'.
(Other definitions for athlete that I've seen before include "Contestant" , "Player" , "One trains in sport" , "Person fit for physical sports" , "gymnast, perhaps" .)