Zombie, regularly drinking - a bit of Oliver Reed is probably in it (4)
I believe the answer is:
oboe
'reed is probably in it' is the definition.
(reed is a part of an oboe)
'zombie regularly drinking a bit of oliver' is the wordplay.
'regularly' indicates alternate letters (regularly take one letter, leave next etc.).
'drinking' means one lot of letters goes inside another.
'a bit of' says to take the initial letters.
The initial letter of 'oliver' is 'o'.
The alternating letters of 'zombie' are 'obe'.
'obe' enclosing 'o' is 'OBOE'.
(Other definitions for oboe that I've seen before include "Double-reed woodwind" , "blow it!" , "Orchestral instrument" , "Producer of notes" , "Player" .)