Head off bits of film by Young Conservatives adopting new dubbing technique (3-4)
I believe the answer is:
lip-sync
'dubbing technique' is the definition.
(means of dubbing dialogue)
'head off bits of film by young conservatives adopting new' is the wordplay.
'head off' means to remove the first letter.
'bits of film' becomes 'clips' (film clips).
'by young conservatives' becomes 'yc' (I can't explain this - if you can you should believe this answer much more).
'adopting' is an insertion indicator.
'new' becomes 'n' (common abbreviation eg NT for New Testament).
'clips' with its first letter taken away is 'lips'.
'yc' placed around 'n' is 'ync'.
'lips'+'ync'='LIP-SYNC'
(Other definitions for lip-sync that I've seen before include "Align mouth movements with recorded speech" , "Audio and video alignment of speech" , "Linking of speaker's mouth movements and voice in filmed recordings" .)