Big-headed pest unloved as a child (4)
I believe the answer is:
brat
'child' is the definition.
(I know that brat is a type of imp)
'big-headed pest' is the wordplay.
'big-headed' becomes 'b' (this might be a standard abbreviation which I don't know about).
'pest' becomes 'rat' (rat can mean a nasty person).
'b'+'rat'='BRAT'
'unloved as a' is the link.
This may not be correct. Some or all of it may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for brat that I've seen before include "Mervyn -- (Titus Groan)" , "Spoilt kid" , "Ill-mannered child" , "Ill-behaved child" , "child - that's a nuisance" .)