Go away with Ivan, perhaps on the quiet! (6)
I believe the answer is:
vanish
'go away' is the definition.
(vanishing is a kind of going away)
'ivan perhaps on the quiet' is the wordplay.
'perhaps' indicates an anagram.
'on' means one lot of letters go next to another.
'the quiet' becomes 'sh' ('sh' is used to tell someone to be quiet).
'ivan' anagrammed gives 'vani'.
'vani'+'sh'='VANISH'
'with' is the link.
(Other definitions for vanish that I've seen before include "Cease to exist" , "Disappear (in a puff of smoke?)" , "Evanesce" , "Disappear suddenly" , "Go missing" .)