River and province on the borders of Louisville (4)
I believe the answer is:
nile
'river' is the definition.
(Nile River is an example)
'province on the borders of louisville' is the wordplay.
'province' becomes 'ni' (I've seen this in other clues).
'on' says to put letters next to each other.
'the borders of' says to hollow out the word (remove centre letters).
'louisville' with its middle taken out is 'le'.
'ni'+'le'='NILE'
'and' is the link.
(Other definitions for nile that I've seen before include "white flower?" , "Cairo's river" , "River of eastern Africa" , "Line (anag)" , "River at Luxor" .)