Parting words starting barely halfway through drunken voicemail (5)
I believe the answer is:
envoi
'parting words' is the definition.
(passage at the end of a literary work)
'starting barely halfway through drunken voicemail' is the wordplay.
'starting barely halfway through' indicates the answer is hidden within the clue (the answer is roughly halfway through the phrase).
'ENVOI' is hidden within 'drunken voicemail'.
(Other definitions for envoi that I've seen before include "Final message" , "Poetic conclusion to book" , "Final stanza in ballad" , "Short concluding stanza" , "Concluding words" .)