Insult by a President at Conference? Make yourself scarce! (9)
I believe the answer is:
disappear
'yourself scarce' is the definition.
I can't tell whether this definition defines the answer.
'insult by a president at conference?' is the wordplay.
'insult' becomes 'dis' (shortened form of 'disrespect' - slang).
'by' means one lot of letters go next to another.
'president' becomes 'p' (common abbreviation eg in VP).
'at' means one lot of letters go next to another.
'conference?' becomes 'pear' (conference pear is a type of pear).
'dis'+'a'+'p'+'pear'='DISAPPEAR'
'make' is the link.
Can you help me to learn more?
(Other definitions for disappear that I've seen before include "Fly" , "go by the board" , "Fade out" , "Escape" , "Become invisible" .)