Family member found in outskirts of Newcastle? That's a relief! (6)
I believe the answer is:
nephew
'family member' is the definition.
'outskirts of newcastle? that's a relief' is the wordplay.
'outskirts of' says to hollow out the word (remove centre letters).
'that's a relief' becomes 'phew'.
'newcastle' with its middle removed is 'ne'.
'ne'+'phew'='NEPHEW'
'found in' acts as a link.
(Other definitions for nephew that I've seen before include "Kinsman" , "Brother's/sister's son" , "Edward V to Richard III relation" , "Sister's son" , "Has a duty (to do something)" .)