Relative ended, oddly, with expression of relief (6)
I believe the answer is:
nephew
'relative' is the definition.
(type of relative)
'ended oddly with expression of relief' is the wordplay.
'oddly' means one should take alternating letters (letters in the odd-numbered positions are used).
'with' means one lot of letters go next to another.
'expression of relief' becomes 'phew' (sound made when relieved).
The alternate letters of 'ended' are 'ne'.
'ne'+'phew'='NEPHEW'
(Other definitions for nephew that I've seen before include "A young male relation" , "Has a duty (to do something)" , "Brother's/sister's son" , "Sister's son" , "A sibling's child" .)