Take drugs with half-cut Liverpudlian (3)
I believe the answer is:
use
'take drugs' is the definition.
(use can mean to take drugs)
'half-cut liverpudlian' is the wordplay.
'half cut' suggests halving the letters.
'liverpudlian' becomes 'scouse' (both mean coming from Liverpool).
'scouse' with half the letters taken is 'USE'.
'with' acts as a link.
(Other definitions for use that I've seen before include "Employ - custom" , "Practise" , "Application" , "Consumption" , "particular church liturgy" .)