Travel north or east, at first, in this state (6)
I believe the answer is:
oregon
'this state' is the definition.
(I've seen this before)
'travel north or east at first' is the wordplay.
'travel' becomes 'go' ('go' can be a synonym of 'travel'**).
'north' becomes 'n' ('N' can be a synonym of 'north').
'east' becomes 'e' ('E' can be a synonym of 'east').
'at first' says to put letters next to each other.
'or'+'e'='ore'
'go'+'n'='gon'
'gon' after 'ore' is 'OREGON'.
'in' is the link.
(Other definitions for oregon that I've seen before include "area of America" , "The American state is no goer, strangely" , "Old trail led here" , "Gooner (anag) - US state" , "American state, capital Salem (6)." .)