A reckoning that comes to nothing (9)
I believe the answer is:
countdown
This clue is a double definition.
'a reckoning' is the first definition.
(I know that countdown is a type of reckoning)
'comes to nothing' is the second definition.
(I've seen this before)
'that' acts as a link.
(Other definitions for countdown that I've seen before include "Run-up" , "Three, two, one - launch spacecraft" , "TV programme" , "game show" , "5-4-3-2-1" .)