Miss a grand perhaps (6)
I believe the answer is:
joanna
'grand perhaps' is the definition.
I can't judge whether this definition defines the answer.
'miss a' is the wordplay.
'miss' becomes 'joann' (I can't explain this - if you can you should give a lot more credence to this answer).
'joann'+'a'='JOANNA'
Can you help me to learn more?
(Other definitions for joanna that I've seen before include "east end piano" , "Piano (rhyming slang)" , "One's played" , "Girl's name, piano" .)