Noise of dog cut short in saloon? (3)
I believe the answer is:
bar
'in saloon?' is the definition.
(I know that bar is part of gin mill)
'noise of dog cut' is the wordplay.
'noise of dog' becomes 'bark' (dogs bark).
'cut' means to remove the last letter.
'bark' with its final letter removed is 'BAR'.
'short' is the link.
(Other definitions for bar that I've seen before include "an amount of pressure" , "Counter in 21" , "Prohibit; pressure unit" , "Pub; restriction" , "sovereign" .)