Carry on to the end (4)
I believe the answer is:
last
I believe this clue is a double definition.
'carry on' is the first definition.
(thesaurus)
'the end' is the second definition.
(I've seen this before)
'to' is the link.
(Other definitions for last that I've seen before include "Bringing up the rear" , "Most unlikely" , "Least likely" , "` `Let the cobbler stick to his ....' '" , "Continue" .)