Perish, failing to finish slimming programme (3)
I believe the answer is:
die
'perish' is the definition.
(synonyms)
'failing to finish slimming programme' is the wordplay.
'failing to finish' means to remove the last letter.
'slimming programme' becomes 'diet' (a diet might make someone slimmer).
'diet' with its last letter removed is 'DIE'.
(Other definitions for die that I've seen before include "THIRD PART OF 24" , "Depart with engraved stamp" , "Cease to exist" , "Pass from physical life" , "One spotted" .)