Quality of a new mitre (5)
I believe the answer is:
merit
'quality' is the definition.
(merit is a kind of quality)
'new mitre' is the wordplay.
'new' is an anagram indicator.
'mitre' with letters rearranged gives 'MERIT'.
'of a' is the link.
(Other definitions for merit that I've seen before include "The M in OM" , "Excellence, worth" , "Excellence that deserves to be honoured" , "Worth; deserve" , "Quality deserving reward" .)