Look after husband's personal growth (4)
I believe the answer is:
hair
'personal growth' is the definition.
(growth on one's person)
'look after husband's' is the wordplay.
'look' becomes 'air' (I've seen this before).
'after' means one lot of letters go next to another.
'husband' becomes 'h'.
'air' after 'h' is 'HAIR'.
(Other definitions for hair that I've seen before include "Fibre; small extent" , "Fur - mop" , "Barnet" , "One's crowning glory?" , "Growth from skin" .)