Musical piece given in public, by river (8)
I believe the answer is:
overture
'musical piece' is the definition.
(I've seen this in another clue)
'public by river' is the wordplay.
'public' becomes 'overt' (both can mean well-known or unconcealed).
'by' means one lot of letters go next to another.
'river' becomes 'ure' (river in Yorkshire).
'overt'+'ure'='OVERTURE'
'given in' acts as a link.
(Other definitions for overture that I've seen before include "Introduction to, eg, an opera" , "Introductory music" , "Music played before an opera" , "Opening gambit" , "Opening music" .)