Follows races with a tight finish (6)
I believe the answer is:
traces
'follows' is the definition.
('trace' can be a synonym of 'follow')
'races with a tight finish' is the wordplay.
'with' means one lot of letters go next to another.
'finish' says to take the final letters.
The last letter of 'tight' is 't'.
'races' after 't' is 'TRACES'.
(Other definitions for traces that I've seen before include "Vestiges (that may be kicked over?)" , "Kick these over to be insubordinate or reckless" , "Finds; signs" , "Just detectable amounts" , "Tracks down or outlines" .)