Scotsman entering river for a grand, perhaps (5)
I believe the answer is:
piano
'a grand perhaps' is the definition.
(grand is a kind of piano)
'scotsman entering river' is the wordplay.
'scotsman' becomes 'ian' (common Scottish name).
'entering' indicates putting letters inside.
'river' becomes 'Po' (Italian river).
'ian' inserted within 'po' is 'PIANO'.
'for' is the link.
(Other definitions for piano that I've seen before include "Soft - musical instrument" , "In musical notation, this means softly" , "Direction in music (1): relatively softly" , "Musical instrument - softly, please" , "Soft, softly (music)" .)