Loudly insult a contemporary and depart (9)
I believe the answer is:
disappear
'depart' is the definition.
(thesaurus)
'loudly insult a contemporary' is the wordplay.
I cannot quite see how this works, but
'insult' could be 'dis' (shortened form of 'disrespect' - slang) and 'dis' is located in the answer.
'a' is found in the answer.
This may be the basis of clue (or it may be nonsense).
'and' acts as a link.
(Other definitions for disappear that I've seen before include "Go missing" , "Vanish, cease to be visible" , "Pass out of sight" , "Fade out" , "Do a bunk" .)