Initiation of a hand during social event (10)
I believe the answer is:
admittance
'initiation' is the definition.
(thesaurus)
'a hand during social event' is the wordplay.
'hand' becomes 'mitt' (synonyms).
'during' indicates putting letters inside.
'social event' becomes 'dance' (I've seen this before).
'mitt' inserted inside 'dance' is 'dmittance'.
'a'+'dmittance'='ADMITTANCE'
'of' acts as a link.
(Other definitions for admittance that I've seen before include "gives one the right to be there" , "Entry" , "Letting in" , "Right to enter" , "What bouncer controls" .)