Sister’s relatives have songbird (6)
I believe the answer is:
siskin
'songbird' is the definition.
(I've seen this before)
'sister's relatives' is the wordplay.
'sister's' becomes 'sis'' ('sis' can be a synonym of 'sister').
'relatives' becomes 'kin' (I've seen this before).
'sis'+'kin'='SISKIN'
'have' acts as a link.
(Other definitions for siskin that I've seen before include "Yellow-green finch" , "Type of bird" , "Small bird - kiss in (anag)" , "Type of finch" , "Small songbird related to the goldfinch" .)