Travel on river — seriously (6)
I believe the answer is:
deeply
'seriously' is the definition.
(thesaurus)
'travel on river' is the wordplay.
'travel' becomes 'ply' (plying is a kind of travelling).
'on' says to put letters next to each other.
'river' becomes 'dee' (River Dee).
'ply' put after 'dee' is 'DEEPLY'.
(Other definitions for deeply that I've seen before include "With profundity" , "With intense feeling" , "In a profound way" , "Intensely" , "fathoms down?" .)