Kitty's daughter chasing light-hearted pleasure (4)
I believe the answer is:
fund
'kitty's' is the definition.
(fund or money for a particular purpose)
'daughter chasing light-hearted pleasure' is the wordplay.
'daughter' becomes 'd' (genealogical abbreviation).
'chasing' means one lot of letters go next to another (some letters chase after others).
'light-hearted pleasure' becomes 'fun' (I've seen this before).
'd' after 'fun' is 'FUND'.
(Other definitions for fund that I've seen before include "Large stock; pay for" , "Stock, resources" , "Supply cash" , "Cash reserve" , "Give money" .)