Second drink and girl's beginning amorous activity (8)
I believe the answer is:
snogging
'amorous activity' is the definition.
'second drink and girl's beginning' is the wordplay.
'second' becomes 's' (common abbreviation).
'drink' becomes 'noggin' (drink measurement, typically a quarter of a pint**).
'and' says to put letters next to each other.
'beginning' says to take the initial letters.
The initial letter of 'girl' is 'g'.
's'+'noggin'+'g'='SNOGGING'
(Other definitions for snogging that I've seen before include "connecting romantically" , "Cuddling, kissing (sl.)" .)