Beer that's mine around noon (4)
I believe the answer is:
pint
'beer' is the definition.
(beer is typically served by the pint)
'mine around noon' is the wordplay.
'mine' becomes 'pit' (down the pit).
'around' means one lot of letters goes inside another.
'noon' becomes 'n'.
'pit' placed around 'n' is 'PINT'.
'that's' acts as a link.
(Other definitions for pint that I've seen before include "small amount" , "Standard measure of beer or milk" , "Imperial measure of capacity" , "Unit of capacity" , "Liquid measure" .)