Poem makes one fairly rich? Not entirely (5)
I believe the answer is:
lyric
'poem' is the definition.
(lyric poem is a kind of poem)
'makes one fairly rich? not entirely' is the wordplay.
'not entirely' indicates the answer is hidden within the clue.
'LYRIC' is hidden within 'makes fairly rich'.
(Other definitions for lyric that I've seen before include "(Of poetry) expressing emotion" , "Words to a song" , "having a light quality" , "Song's words" , "Expressing personal feelings" .)