Engaged in the writer’s revolutionary musical (5)
I believe the answer is:
evita
'musical' is the definition.
(Andrew Lloyd Webber musical)
'engaged in the writer's revolutionary' is the wordplay.
'engaged in' becomes 'at' (to be 'at' a task is to be engaged in doing it).
'the writer's' becomes 'ive' ('I have' could mean 'the writer has').
'revolutionary' says the letters should be written in reverse (letters revolve around).
'at'+'ive'='ative'
'ative' written backwards gives 'EVITA'.
(Other definitions for evita that I've seen before include "Peron musical" , "Show" , "1996 musical film, starring Madonna" , "Musical based on Argentine leader" , "Nineteen Dn musical" .)