Close to herbaceous border plant (5)
I believe the answer is:
sedge
'plant' is the definition.
The answer is an example.
'close to herbaceous border' is the wordplay.
'close to' says to take the final letters (the close/ending of).
'border' becomes 'edge' ('edge' can be a synonym of 'border').
The last letter of 'herbaceous' is 's'.
's'+'edge'='SEDGE'
(Other definitions for sedge that I've seen before include "plant with triangular stems" , "Coarse grassy plant" , "Grass-like plant growing in marshes" , "Waterside plant" , "Marsh-dweller" .)