Outsiders in Wichita providing for neglected child (4)
I believe the answer is:
waif
'neglected child' is the definition.
(I've seen this before)
'outsiders in wichita providing' is the wordplay.
'outsiders in' suggests removing the centre.
'providing' becomes 'if' (I've seen this in other clues).
'wichita' with its middle taken out is 'wa'.
'wa'+'if'='WAIF'
'for' is the link.
(Other definitions for waif that I've seen before include "Orphan" , "Someone very thin or underfed" , "Foundling" , "Gamin" , "Homeless child - thin person" .)