Obscure country’s losing a contest finally in court (10)
I believe the answer is:
indistinct
'obscure' is the definition.
(thesaurus)
'in court' is the wordplay.
'court' becomes 'distinct' (I can't justify this - if you can you should give a lot more credence to this answer).
'in'+'distinct'='INDISTINCT'
'country's losing a contest finally' acts as a link.
I am not very happy about this link. Some or all of it may belong to another bit of the clue.
(Other definitions for indistinct that I've seen before include "Not clearly defined" , "Obscure" , "Blurred" .)