Relative backing of measure that's a relief (6)
I believe the answer is:
nephew
'relative' is the definition.
(type of relative)
'backing of measure that's a relief' is the wordplay.
'backing of' says the letters should be written backwards.
'measure' becomes 'en' (typographical measure).
'that's a relief' becomes 'phew' (phew is an expression of relief).
'en' written backwards gives 'ne'.
'ne'+'phew'='NEPHEW'
(Other definitions for nephew that I've seen before include "Edward V to Richard III relation" , "Family relative" , "Sibling's son" , "A sibling's child" , "Male relative" .)