A bighead, some new broom (5)

I believe the answer is:

besom

'broom' is the definition.
(besom is a kind of broom)

'a bighead some new' is the wordplay.
'a bighead' becomes 'b' (the head letter of 'big').
'new' indicates an anagram.
'some' is an anagram of 'esom'.
'b'+'esom'='BESOM'

(Other definitions for besom that I've seen before include "Twiggy broom" , "Concoction of twigs" , "Broom made from twigs tied to a handle" , "sweeps with it?" , "I sweep" .)

I've seen this clue in the Evening Standard.

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