One particular exercise poet doesn't finish (6)
I believe the answer is:
pedant
'one particular' is the definition.
(I've seen this before)
'exercise poet doesn't finish' is the wordplay.
'exercise' becomes 'pe' (Physical Education).
'poet' becomes 'Dante' (13th- and 14th-century Italian poet).
'doesn't finish' means to remove the last letter.
'dante' with its last letter taken away is 'dant'.
'pe'+'dant'='PEDANT'
(Other definitions for pedant that I've seen before include "One who insists on minor details, may be a conceited know-all" , "formalist" , "One pays undue attention to the petty details" , "Fussy schoolmaster, academic" , "Stickler for trivial detail" .)