Finish close second in race (8)
I believe the answer is:
complete
'finish' is the definition.
(I know that finish can be written as complete)
'close second in race' is the wordplay.
'close second' becomes 'l' (2nd letter of 'close').
'in' is an insertion indicator.
'race' becomes 'compete' (compete in a race).
'l' placed inside 'compete' is 'COMPLETE'.
(Other definitions for complete that I've seen before include "Finished, entire" , "Finish; whole" , "Having all the necessary parts" , "Polish off" , "Whole, entire, uncut" .)