Sharpen up after second trip on the river (5)
I believe the answer is:
rhone
'the river' is the definition.
(Rhone is an example)
'sharpen up after second trip' is the wordplay.
'sharpen up' becomes 'hone' (I've seen this in another clue).
'after' says to put letters next to each other.
'second trip' becomes 'r' (2nd letter of 'trip').
'hone' put after 'r' is 'RHONE'.
'on' is the link.
(Other definitions for rhone that I've seen before include "European river and glacier" , "Swiss-French river" , "12 wine region" , "Current" , "River flowing through Lake Geneva" .)