Tramp primarily has overpowering personal whiff (4)
I believe the answer is:
hobo
'tramp' is the definition.
(both can mean a homeless person)
'primarily has overpowering personal whiff' is the wordplay.
'primarily' says to take the initial letters.
'overpowering personal whiff' becomes 'obo' (I can't explain this - if you can you should believe this answer much more).
The first letter of 'has' is 'h'.
'h'+'obo'='HOBO'
Can you help me to learn more?
(Other definitions for hobo that I've seen before include "American tramp" , "Homeless American" , "Vagrant (American)" , "Vagrant, tramp" , "Deer, situated at the back" .)