Yorkshire river leaks out of its banks (6)
I believe the answer is:
ribble
'yorkshire river' is the definition.
(the Ribble runs through North Yorkshire)
'leaks out of its banks' is the wordplay.
'leaks' becomes 'dribbles'.
'out of its banks' means to look at the middle letters (the edges or 'banks' of the word are removed).
The central letters of 'dribbles' are 'RIBBLE'.
(Other definitions for ribble that I've seen before include "River at Preston" , "Preston's river" .)