Diana goes to the museum to see the prima donna (4)
I believe the answer is:
diva
'the prima donna' is the definition.
(I know this)
'diana goes to the museum' is the wordplay.
'diana' becomes 'Di' (Di is short for Diana).
'goes to' is a charade indicator (letters next to each other).
'the museum' becomes 'VA' (Victoria and Albert Museum, or 'V and A').
'di'+'va'='DIVA'
'to see' acts as a link.
(Other definitions for diva that I've seen before include "Long narrow top" , "Distinguished female singer" , "For example Sutherland" , "Great performer" , "A female opera singer" .)