Turn up heat and run off (7)
I believe the answer is:
unearth
'turn up' is the definition.
('unearth' can be a synonym of 'turn up')
'heat and run off' is the wordplay.
'and' means one lot of letters go next to another (I've seen this in other clues).
'off' is an anagram indicator.
'heat' after 'run' is 'runheat'.
'runheat' is an anagram of 'UNEARTH'.
(Other definitions for unearth that I've seen before include "Track down" , "Exhume" , "Bring out of obscurity" , "Dig up for a hunter" , "Disconnect terminal" .)