I'm amused about cold area in pub (5)
I believe the answer is:
local
'pub' is the definition.
(one's local pub)
'i'm amused about cold area' is the wordplay.
'i'm amused' becomes 'lol' (abbreviation for laughing out loud).
'about' is an insertion indicator.
'cold' becomes 'C' (eg on taps).
'area' becomes 'a' (maths abbreviation).
'c'+'a'='ca'
'lol' placed around 'ca' is 'LOCAL'.
'in' acts as a link.
(Other definitions for local that I've seen before include "hearing" , "Pub, maybe" , "Belonging to a particular place" , "bar" , "Relating to the neighbourhood" .)