Expression of relief after one leaves old relative (6)
I believe the answer is:
nephew
'relative' is the definition.
(type of relative)
'expression of relief after one leaves old' is the wordplay.
'expression of relief' becomes 'phew' (sound made when relieved).
'after' is a charade indicator (letters next to each other).
'leaves' suggests deleting specific letters.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'one' with 'o' taken away is 'ne'.
'phew' after 'ne' is 'NEPHEW'.
(Other definitions for nephew that I've seen before include "Sibling's son" , "Male relative" , "A sibling's child" , "Sister's son" , "Kinsman" .)