Part of serial is appearing after record and poem (7)
I believe the answer is:
episode
'part of serial' is the definition.
('episode' is part of 'serial')
'is appearing after record and poem' is the wordplay.
'appearing after' says to put letters next to each other.
'record' becomes 'ep'.
'and' means one lot of letters go next to another.
'poem' becomes 'ode' (ode is a kind of poem).
'is' put after 'ep' is 'epis'.
'epis'+'ode'='EPISODE'
(Other definitions for episode that I've seen before include "Distinctive happening" , "Event or series of events in a story" , "One of a related series of events" , "Musical passage" , "from longer work" .)