Near the end (5)

I believe the answer is:

I believe this is a double definition.

'near' is the first definition.
('close' can be a synonym of 'near')

'the end' is the second definition.
(I've seen this before)

(Other definitions for close that I've seen before include "block, > unventilated" , "Cessation" , "Imminent" , "Approaching - tight - finish" , "Heavy" .)

I've seen this clue in the L.A. Times Daily, the Evening Standard and The Times.

Want a hint initially instead of a full solution? Install my app