Move slowly to the brink (4)
I believe the answer is:
edge
This clue is a double definition.
'move slowly' is the first definition.
(I've seen this before)
'the brink' is the second definition.
(thesaurus)
'to' acts as a link.
(Other definitions for edge that I've seen before include "Border, fringe" , "small advantage" , "Sidle, lip" , "Move carefully; limit" , "Keenness" .)