Princess, one travelling east in Gulf State (4)
I believe the answer is:
rani
'princess' is the definition.
(I've seen this before)
'one travelling east in gulf state' is the wordplay.
I cannot quite understand how this works, but
'one' could be 'an' ('a' and 'an' can mean 'one') and 'an' is present in the answer.
'state' could be 'ri' (Rhode Island abbreviation) and 'ri' is found within the remaining letters.
This accounts for all the letters.
This explanation may well be incorrect...
(Other definitions for rani that I've seen before include "Royal Indian female" , "Raja's queen" , "Indian queen" , "Member of royal family" , "Wife of a rajah" .)