Give weary maiden backing to achieve a good grade (5)
I believe the answer is:
merit
'a good grade' is the definition.
(merit means a good mark)
'give weary maiden backing' is the wordplay.
'give' is a charade indicator (letters next to each other).
'weary' becomes 'tire' (synonyms).
'maiden' becomes 'm' (cricket abbreviation).
'backing' says the letters should be written backwards.
'tire' put next to 'm' is 'tirem'.
'tirem' back-to-front is 'MERIT'.
'to achieve' is the link.
(Other definitions for merit that I've seen before include "Quality deserving reward" , "Just deserts" , "Value" , "The M in OM" , "Excellence, desert" .)