Officially, he takes a month over a piece of work (5)
I believe the answer is:
mayor
'officially he' is the definition.
The answer is a person as well as being a singular noun. This is suggested by the definition.
'a month over a piece of work' is the wordplay.
'a month' becomes 'May' (May is an example).
'over' means one lot of letters go next to another.
'a piece of work' becomes 'or' (I can't explain this - if you can you should believe this answer much more).
'may'+'or'='MAYOR'
'takes' acts as a link.
Can you help me to learn more?
(Other definitions for mayor that I've seen before include "For example, Henchard" , "Municipal official" , "Town dignitary" , "Town council head" , "Corporation head" .)