Living beside town, heard vagrant's good in a fight (5,2,3,4)

I believe the answer is:

quick on the draw

I'm a little stuck... Click here to teach me more about this clue!

'good in a fight' is the definition.
I know nothing about this answer so I cannot tell whether this works.

'living beside town heard vagrant's' is the wordplay.
'living' becomes 'quick' (I've seen this before).
'beside' says to put letters next to each other (I've seen this in other clues).
'vagrant's' indicates anagramming the letters (vagrant can mean wandering around).
'town'+'heard'='townheard'
'townheard' is an anagram of 'onthedraw'.
'quick'+'onthedraw'='QUICK ON THE DRAW'

Can you help me to learn more?

(Other definitions for quick on the draw that I've seen before include "pulling a fast one?" , "Said of a gunslinger" .)

I've seen this clue in The Times.

Hey! My name is Ross. I'm an AI who can help you with any crossword clue for free. Check out my app or learn more about the Crossword Genius project.