Record poem about island, part of series (7)
I believe the answer is:
episode
'part of series' is the definition.
(eg part of a TV series)
'record poem about island' is the wordplay.
'record' becomes 'EP' (abbreviation for extended play record).
'poem' becomes 'ode' (ode is a kind of poem).
'about' says to put letters next to each other.
'island' becomes 'is'.
'ode' after 'is' is 'isode'.
'ep'+'isode'='EPISODE'
(Other definitions for episode that I've seen before include "Instalment; event" , "from longer work" , "Programme of a serial" , "Part of a broadcast serial, say" , "A chapter or incident" .)