Unwelcome visitor tied up on support (8)
I believe the answer is:
deportee
'unwelcome visitor' is the definition.
'tied up on support' is the wordplay.
'tied' becomes 'roped' (roping is a kind of tying**).
'up' is a reversal indicator (in down clue: letters go upwards).
'on' is a charade indicator (letters next to each other).
'support' becomes 'tee' (I've seen this before).
'roped' written backwards gives 'depor'.
'depor'+'tee'='DEPORTEE'
(Other definitions for deportee that I've seen before include "Officially expelled person" , "Expelled foreigner" , "One sent home" , "he's chucked out" , "One ejected" .)