Put up with Ned possibly being terribly rude (7)
I believe the answer is:
endured
'put up with' is the definition.
(I've seen this before)
'ned possibly being terribly rude' is the wordplay.
'possibly' indicates an anagram.
'being terribly' indicates anagramming the letters.
'ned' anagrammed gives 'end'.
'rude' anagrammed gives 'ured'.
'end'+'ured'='ENDURED'
(Other definitions for endured that I've seen before include "Put up with something" , "Carried on" , "Borne" , "Red nude (anag.)" , "Bore; put up with" .)