The closing part of the last letter (6)
I believe the answer is:
finale
'the closing' is the definition.
(finale is a kind of closing)
'the last letter' is the wordplay.
'the last' becomes 'final' (I've seen this in another clue).
'letter' becomes 'e' ().
'final'+'e'='FINALE'
'part of' is the link.
(Other definitions for finale that I've seen before include "When it's grand, it's the last scene" , "Ending" , "In leaf (anag.)" , "Last section of a musical composition" , "Conclusion, end" .)