Acorn eater rather a dull chap, I hear (4)
I believe the answer is:
boar
'acorn eater' is the definition.
(boars may eat acorns)
'rather a dull chap i hear' is the wordplay.
'rather a dull chap' becomes 'bore' (a boring person).
'i hear' shows a homophone (sound like).
'bore' is a homophone of 'BOAR'.
(Other definitions for boar that I've seen before include "Resting place for birds or bats" , "Wild swine" , "The head for drink Falstaff had" , "Wild animal, sounds like drill" , "A wild male pig" .)