Heard dullard is a swine (4)
I believe the answer is:
boar
'swine' is the definition.
(male pig)
'heard dullard' is the wordplay.
'heard' indicates a 'sounds like' (homophone) clue.
'dullard' becomes 'bore' (synonyms).
'bore' is a homophone of 'BOAR'.
'is a' acts as a link.
(Other definitions for boar that I've seen before include "A male pig, sounds tedious" , "Uncastrated male pig" , "A wild male pig" , "Wild animal, sounds like drill" , "Sow's mate" .)