An old hand not upset very quickly (6)
I believe the answer is:
pronto
'quickly' is the definition.
(I've seen this before)
'an old hand not upset' is the wordplay.
'an old hand' becomes 'pro' (I've seen this in other clues).
'upset' is an anagram indicator.
'not' anagrammed gives 'nto'.
'pro'+'nto'='PRONTO'
'very' acts as a link.
(Other definitions for pronto that I've seen before include "Immediately, amigo" , "Double quick!" , "Quick as you can, amigo" , "Proton (anag.)" , "Quickly, amigo" .)