Record one's poem for instalment (7)
I believe the answer is:
episode
'for instalment' is the definition.
(synonyms)
'record one's poem' is the wordplay.
'record' becomes 'EP' (abbreviation for extended play record).
'one's' becomes 'i's' (Roman numeral).
'poem' becomes 'ode' (ode is a type of poem).
'ep'+'is'+'ode'='EPISODE'
(Other definitions for episode that I've seen before include "Programme of a serial" , "Distinctive incident" , "Event or series of events in a story" , "Incident or event as part of sequence" , "One part of a serial" .)