Quick hugs provided calm (6)
I believe the answer is:
pacify
'calm' is the definition.
(I know that pacify is a kind of calm)
'quick hugs provided' is the wordplay.
'quick' becomes 'pacy'.
'hugs' is an insertion indicator.
'provided' becomes 'if' (eg 'provided it's sunny' means 'if it's sunny').
'pacy' enclosing 'if' is 'PACIFY'.
(Other definitions for pacify that I've seen before include "Make calm, appease" , "Quieten" , "Quell the anger of" , "Bring peace to (a place)" , "Placate, calm" .)