Blairite hated being “out” — wanting to be this? (13)
I believe the answer is:
rehabilitated
'to be this?' is the definition.
The definition suggests a singular noun but the answer is not.
'blairite hated being out' is the wordplay.
'being out' is an anagram indicator (out can mean wrong or inaccurate).
'blairite'+'hated'='blairitehated'
'blairitehated' anagrammed gives 'REHABILITATED'.
'wanting' acts as a link.
(Other definitions for rehabilitated that I've seen before include "Helped to readapt" , "Restored to normal functioning" , "Helped back into society" .)