Women's Aid initially provided for homeless child (4)
I believe the answer is:
waif
'homeless child' is the definition.
(I've seen this before)
'women's aid initially provided' is the wordplay.
'initially' indicates taking the first letters.
'provided' becomes 'if'.
The initial letters of 'womens aid' is 'wa'.
'wa'+'if'='WAIF'
'for' acts as a link.
(Other definitions for waif that I've seen before include "Be incongruous" , "Orphan" , "Foundling" , "Gamin" , "Someone very thin or underfed" .)