British traitor was problem child (4)
I believe the answer is:
brat
'problem child' is the definition.
'brat' can be an answer for 'child' (brat is a kind of child). I am not certain of the 'problem' bit.
'british traitor' is the wordplay.
'british' becomes 'b' (abbreviation e.g. in BBC).
'traitor' becomes 'rat' (rat can mean a treacherous person).
'b'+'rat'='BRAT'
'was' acts as a link.
Can you help me to learn more?
(Other definitions for brat that I've seen before include "Ill-mannered child" , "Unpleasant child" , "Spoilt kid" , "Nasty little kid" , "Spoilt child" .)