Converged around border (5)
I believe the answer is:
verge
'border' is the definition.
(I know that verge is a type of border)
'converged around' is the wordplay.
'around' indicates the answer is hidden within the clue.
'VERGE' is hidden within 'converged'.
(Other definitions for verge that I've seen before include "Margin, edge" , "Border - edge" , "Margin or brink" , "Grass border along road" , "Grass edge to road" .)