Deserved to finish the summer on a fancy diet (7)
I believe the answer is:
merited
'deserved' is the definition.
(I know that deserved can be written as merited)
'finish the summer on a fancy diet' is the wordplay.
'finish' means to take half the letters.
'on' is a charade indicator (letters next to each other).
'a fancy' indicates anagramming the letters.
'summer' halved is 'mer'.
'diet' is an anagram of 'ited'.
'mer'+'ited'='MERITED'
'to' acts as a link.
(Other definitions for merited that I've seen before include "Deresved" , "appropriate" , "Was worthy" , "Properly earned or deserved" .)