One doing wilful damage in museum close to Whitehall (6)
I believe the answer is:
vandal
'one doing wilful damage' is the definition.
(criminal who damages things)
'museum close to whitehall' is the wordplay.
'museum' becomes 'V and A' (Victoria and Albert Museum).
'close to' indicates one should take the final letters (the 'close' to the word).
The last letter of 'whitehall' is 'l'.
'vanda'+'l'='VANDAL'
'in' is the link.
(Other definitions for vandal that I've seen before include "Destroyer or defacer of property" , "One of those who sacked Rome in 455" , "Wanton wrecker" , "Cultural destroyer" , "One who maliciously causes damage" .)