Drunk giant swallows large cocktail or that's what they're saying (7)
I believe the answer is:
talking
'that's what they're saying' is the definition.
The definition suggests an adverb but the answer is not.
'drunk giant swallows large cocktail' is the wordplay.
'drunk' indicates an anagram.
'swallows' means one lot of letters goes inside another.
'large' becomes 'l'.
'cocktail' becomes 'k' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'giant' with letters rearranged gives 'taing'.
'l'+'k'='lk'
'taing' placed around 'lk' is 'TALKING'.
'or' is the link.
Can you help me to learn more?
(Other definitions for talking that I've seen before include "Speaking" , "Chatting" , "Conversing" , "Verbalising" .)