Will he grow up a bigheaded rotter? (4)
I believe the answer is:
brat
'will he grow up a' is the definition.
The answer is a person as well as being a singular noun. This is suggested by the definition.
'bigheaded rotter?' is the wordplay.
'bigheaded' becomes 'b' (this could be a standard abbreviation I've not previously seen).
'rotter?' becomes 'rat' ('rat' can be a synonym of 'rotter').
'b'+'rat'='BRAT'
Can you help me to learn more?
(Other definitions for brat that I've seen before include "Nasty child" , "Troublesome child" , "Spoilt child" , "Very dry" , "Nasty little kid" .)