Relative value not nice, odd bits thrown away (6)
I believe the answer is:
auntie
'relative' is the definition.
(auntie is a kind of relative)
'value not nice odd bits thrown away' is the wordplay.
'odd bits thrown away' indicates alternate letters (letters in odd-numbered positions removed).
'value'+'not'+'nice'='valuenotnice'
The alternating letters of 'valuenotnice' are 'AUNTIE'.
(Other definitions for auntie that I've seen before include "BBC nickname" , "Kinswoman" , "Relation; the BBC" , "The Beeb" , "Family relative" .)