Drink bottles beginning to affect party game (9)
I believe the answer is:
paintball
'game' is the definition.
(I've seen this before)
'drink bottles beginning to affect party' is the wordplay.
'drink' becomes 'pint' (pint is a unit of liquid volume).
'bottles' means one lot of letters goes inside another (bottle can mean to contain).
'beginning to' indicates taking the first letters.
'party' becomes 'ball' (ball is a kind of party).
The initial letter of 'affect' is 'a'.
'pint' enclosing 'a' is 'paint'.
'paint'+'ball'='PAINTBALL'
(Other definitions for paintball that I've seen before include "Missile used in war games" , "war game" , "messy game" , "simulated combat" .)