Cook slowly heading off in rear (5)
I believe the answer is:
raise
'rear' is the definition.
(synonyms)
'cook slowly heading off' is the wordplay.
'cook slowly' becomes 'braise' (I've seen this in another clue).
'heading off' means to remove the first letter.
'braise' with its first letter taken off is 'RAISE'.
'in' is the link.
(Other definitions for raise that I've seen before include "Aries (anag)" , "Haul up" , "More money from America" , "Increased earnings in America" , "Cultivate by growing" .)