Built a join oddly with rejoicing (10)
I believe the answer is:
jubilation
'rejoicing' is the definition.
(I know that rejoicing can be written as jubilation)
'built a join oddly' is the wordplay.
'oddly' indicates anagramming the letters (letters in an odd order).
'built'+'a'+'join'='builtajoin'
'builtajoin' anagrammed gives 'JUBILATION'.
'with' acts as a link.
(Other definitions for jubilation that I've seen before include "Joy" , "Triumphal rejoicing" .)