Liverpudlian applying science to river (6)
I believe the answer is:
scouse
'liverpudlian' is the definition.
(both mean coming from Liverpool)
'science to river' is the wordplay.
'science' becomes 'sc'.
'to river' becomes 'ouse' (Yorkshire river).
'sc'+'ouse'='SCOUSE'
'applying' acts as a link.
(Other definitions for scouse that I've seen before include "Liverpudlian (colloq.)" , "Slang for native of Liverpool" , "another city's dialect" , "Liverpool accent" , "English dialect spoken in Liverpool" .)