Tweet cover of Prince record (4)
I believe the answer is:
peep
'tweet' is the definition.
(thesaurus)
'cover of prince record' is the wordplay.
'cover of' suggests removing the centre (only the letters which cover the word).
'record' becomes 'EP' (abbreviation for extended play record).
'prince' with its middle removed is 'pe'.
'pe'+'ep'='PEEP'
(Other definitions for peep that I've seen before include "Look surreptitiously - through a keyhole?" , "Look slyly" , "Look surreptitiously, like Tom" , "Chirp" , "Secret look" .)