Royalist travelling alone (8)
I believe the answer is:
solitary
'alone' is the definition.
('solitary' can be a synonym of 'alone')
'royalist travelling' is the wordplay.
'travelling' indicates an anagram.
'royalist' with letters rearranged gives 'SOLITARY'.
(Other definitions for solitary that I've seen before include "reclusive" , "Secluded, isolated" , "Lacking companions" , "Recluse" , "Being the only one" .)