Objective Kennedy oddly rejected (3)
I believe the answer is:
end
'objective' is the definition.
(thesaurus)
'kennedy oddly rejected' is the wordplay.
'oddly rejected' indicates alternate letters.
The alternate letters of 'kennedy' are 'END'.
(Other definitions for end that I've seen before include "Limit" , "Objective or conclusion" , "Novel by Graham Greene" , "Extremity" , "Conclusion or purpose" .)