Student is man primarily behind museum defacement (9)
I believe the answer is:
vandalism
'defacement' is the definition.
(I know that defacement can be written as vandalism)
'student is man primarily behind museum' is the wordplay.
'student' becomes 'l' (as in L-plates for learner drivers).
'primarily' suggests taking the first letters.
'behind' says to put letters next to each other.
'museum' becomes 'vanda' (Victoria and Albert Museum).
The first letter of 'man' is 'm'.
'l'+'is'+'m'='lism'
'lism' after 'vanda' is 'VANDALISM'.
(Other definitions for vandalism that I've seen before include "Deliberate destruction" , "property crime" , "Wanton damage" , "Graffiti artist's work" , "Wanton destruction" .)