Old Bill, or Robert (5)
I believe the answer is:
bobby
'old bill' is the definition.
Although both the answer and definition are singular nouns, I can't see how they can define each other.
'robert' is the wordplay.
I cannot quite understand how this works, but
'robert' could be 'bob' (short for Robert) and 'bob' is present in the answer.
The remaining letters 'by' is a valid word which might be clued in a way I don't see.
This explanation may well be incorrect...
'or' acts as a link.
Can you help me to learn more?
(Other definitions for bobby that I've seen before include "Cop (slang)" , "beat man" , "Policeman (sl.)" , "(Local) policeman" , "Rob" .)