Several problems with our visa (7)
I believe the answer is:
various
'several' is the definition.
(I know that several can be written as various)
'problems with our visa' is the wordplay.
'problems' indicates an anagram (I've seen this in other clues).
'with' is a charade indicator (letters next to each other).
'our'+'visa' is 'ourvisa'.
'ourvisa' with letters rearranged gives 'VARIOUS'.
(Other definitions for various that I've seen before include "Divers" , "More than one" , "Disparate, diverse" , "Saviour (anag) -- assorted" , "Of several different kinds" .)