Partly skimp airing leading to damage (6)
I believe the answer is:
impair
'damage' is the definition.
(impairing is a kind of damaging)
'partly skimp airing leading' is the wordplay.
'partly' says the answer is hidden in the clue.
'IMPAIR' can be found hidden inside 'skimp airing leading'.
'to' acts as a link.
(Other definitions for impair that I've seen before include "'Mar, spoil (6)'" , "'Mar, damage (6)'" , "Reduce" , "Hurt or handicap" , "Harm" .)