Finally out to win the double (4)
I believe the answer is:
twin
'the double' is the definition.
(twin can mean someone's double)
'finally out to win' is the wordplay.
'finally' suggests the final letters.
The final letter of 'out' is 't'.
't'+'win'='TWIN'
(Other definitions for twin that I've seen before include "Dead ringer" , "One of two conceived together" , "One of two born together" , "(Town) paired with another" , "Balearic island" .)