The fattest destructive insect is going after fruit (8)
I believe the answer is:
plumpest
'the fattest' is the definition.
I can't tell whether this defines the answer.
'destructive insect is going after fruit' is the wordplay.
'destructive insect' becomes 'pest' (I've seen this before).
'is going after' means one lot of letters go next to another.
'fruit' becomes 'plum' (plum is a kind of fruit).
'pest' put after 'plum' is 'PLUMPEST'.
Can you help me to learn more?
(Another definition for plumpest that I've seen is " better fed than the rest?".)