Tight finish (5)

I believe the answer is:

I believe this clue is a double definition.

'tight' is the first definition.
(I know that tight can be written as close)

'finish' is the second definition.
(I know that finish can be written as close)

(Other definitions for close that I've seen before include "on very affectionate terms" , "cathedral precinct" , "Approaching - tight - finish" , "cul-de-sac" , "Tightly" .)

I've seen this clue in The Telegraph, The Guardian and The Irish News.

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