That fellow greeting mayor at the front (3)
I believe the answer is:
him
'that fellow' is the definition.
('him' refers to a man)
'greeting mayor at the front' is the wordplay.
'greeting' becomes 'hi' (hi is a kind of greeting).
'at the front' suggests taking the first letters.
The first letter of 'mayor' is 'm'.
'hi'+'m'='HIM'
(Other definitions for him that I've seen before include "Objective male pronoun" , "That man" , "Proper character" .)