Destructive type in museum then left (6)
I believe the answer is:
vandal
'destructive type' is the definition.
(I've seen this before)
'in museum then left' is the wordplay.
'in' means one lot of letters goes inside another.
'museum' becomes 'va' (Victoria and Albert Museum, or 'V and A').
'then' becomes 'and' ('and then' can be a synonym of 'then').
'left' becomes 'l' (common abbreviation).
'va' enclosing 'and' is 'vanda'.
'vanda'+'l'='VANDAL'
(Other definitions for vandal that I've seen before include "Hooligan" , "Person causing destruction to property" , "He breaks things wantonly" , "Person causing wanton damage" , "Person who maliciously damages things" .)