Taper off a sort of true poet (5,3)
I believe the answer is:
peter out
'taper off' is the definition.
(synonyms)
'a sort of true poet' is the wordplay.
'a sort of' is an anagram indicator.
'true'+'poet'='truepoet'
'truepoet' anagrammed gives 'PETER OUT'.
(Other definitions for peter out that I've seen before include "'Run down, taper off (5,3)'" , "Dwindle away to nothing" , "Diminish feebly" , "True poet (anag) - come to nothing" , "End gradually" .)