Carrying a little gun does improve one’s disposition (7)
I believe the answer is:
sweeten
'improve one's disposition' is the definition.
I can't judge whether this defines the answer.
'carrying a little gun' is the wordplay.
'carrying' means one lot of letters goes inside another.
'a little' becomes 'wee' (I've seen this before).
'gun' becomes 'sten' (British sub-machine gun).
'wee' placed inside 'sten' is 'SWEETEN'.
'does' is the link.
Can you help me to learn more?
(Other definitions for sweeten that I've seen before include "Make less bitter" , "pacify!" , "Seen wet (anag.)" , "put in sugar" , "Add, eg, sugar to" .)