Slight temptation, briefly, after beginning to slim (4)
I believe the answer is:
slur
'slight' is the definition.
(I've seen this in another clue)
'temptation briefly after beginning to slim' is the wordplay.
'temptation' becomes 'lure' (lure is a kind of temptation).
'briefly' means to remove the last letter.
'after' means one lot of letters go next to another.
'beginning to' indicates taking the first letters.
The first letter of 'slim' is 's'.
'lure' with its final letter taken off is 'lur'.
'lur' after 's' is 'SLUR'.
(Other definitions for slur that I've seen before include "Speak as drunk perhaps" , "Musical sign: "Run together"" , "Discredit, say reputation" , "Disparage" , "Slight - smear" .)