Finished first in that Open? (5)
I believe the answer is:
overt
'open?' is the definition.
('overt' is associated in meaning with 'open')
'finished first in that' is the wordplay.
'finished' becomes 'over' (similar in meaning).
'first in that' becomes 't' (1st letter of 'that').
'over'+'t'='OVERT'
(Other definitions for overt that I've seen before include "Openly displayed" , "Not concealed - public" , "Done or shown openly" , "Open and candid" , "Trove (anag.)" .)