Sounds like pig is a nuisance (4)
I believe the answer is:
bore
'nuisance' is the definition.
(I've seen this before)
'sounds like pig' is the wordplay.
'sounds like' shows a homophone (sound like).
'pig' becomes 'boar' (male pig).
'boar' is a homophone of 'BORE'.
'is a' is the link.
(Other definitions for bore that I've seen before include "Dull person; hole" , "Push through a crowd" , "Make a hole with a pointed tool" , "pain from > drill" , "Drill or weary" .)