He may take up your case at the end of the day (5,6)
I believe the answer is:
night porter
'he may take up your' is the definition.
The answer is a person as well as being a singular noun. This is suggested by the definition.
'case at the end of the day' is the wordplay.
'case' becomes 'porter' (I can't explain this - if you can you should give a lot more credence to this answer).
'at' is a charade indicator (letters next to each other) (I've seen this in other clues).
'the end of the day' becomes 'night' (night follows day).
'porter' after 'night' is 'NIGHT-PORTER'.
Can you help me to learn more?
(Another definition for night porter that I've seen is " Building attendant for the hours of darkness".)