Adult cut out youth's centre parting (5)
I believe the answer is:
adieu
'parting' is the definition.
(thesaurus)
'adult cut out youth's centre' is the wordplay.
'adult' becomes 'a' (abbreviation).
'cut out' becomes 'die' (dying is a kind of cutting out).
'centre' says to take the centre.
The middle of 'youth' is 'u'.
'a'+'die'+'u'='ADIEU'
(Other definitions for adieu that I've seen before include "left, making this?" , "Goodbye, monsieur" , "Goodbye, mademoiselle" , "So long abroad" , "Adios, Arrivederci" .)