Relative gets a quarter - that's a relief! (6)
I believe the answer is:
nephew
'relative' is the definition.
(nephew is a kind of relative)
'a quarter that's a relief' is the wordplay.
'a quarter' becomes 'ne'.
'that's a relief' becomes 'phew'.
'ne'+'phew'='NEPHEW'
'gets' acts as a link.
(Other definitions for nephew that I've seen before include "Sibling's son" , "Kinsman" , "Has a duty (to do something)" , "Family relative" , "Brother's/sister's son" .)