Evasively holding up entry permit (4)
I believe the answer is:
visa
'entry permit' is the definition.
(I've seen this in another clue)
'evasively holding up' is the wordplay.
'holding' indicates the answer is hidden within the clue.
'up' says the letters should be written in reverse (in down clue: letters go upwards).
'asiv' is hidden within 'evasively'.
'asiv' in reverse letter order is 'VISA'.
(Other definitions for visa that I've seen before include "Authorisation to enter a country" , "Passport stamp or well-known credit card" , "Addition to passport" , "Travel stamp in passport" , "ID" .)