Thrashing ending in remorse, that's the way! (5)
I believe the answer is:
route
'the way' is the definition.
(route is a kind of way)
'thrashing ending in remorse' is the wordplay.
'thrashing' becomes 'rout'.
'ending in' indicates one should take the final letters.
The last letter of 'remorse' is 'e'.
'rout'+'e'='ROUTE'
'that's' is the link.
(Other definitions for route that I've seen before include "Course to be travelled" , "Course, path" , "Itinerary; way" , "Way, path" , "Path to follow" .)