Just arrived in an insignificant place (7)
I believe the answer is:
nowhere
'place' is the definition.
(I have seen 'Nonexistent place' mean 'nowhere' so perhaps 'place' could also mean 'nowhere')
I don't understand how the remainder of the clue works.
(Other definitions for nowhere that I've seen before include "Neither here nor there?" , "no prospect of success" , "Erewhon (anag.)" , "Remote or uninteresting place" , "Miles behind!" .)