Adrian is travelling to reach Mediterranean island (8)
I believe the answer is:
sardinia
'mediterranean island' is the definition.
(I've seen this before)
'adrian is travelling' is the wordplay.
'travelling' indicates an anagram.
'adrian'+'is'='adrianis'
'adrianis' with letters rearranged gives 'SARDINIA'.
'to reach' is the link.
(Other definitions for sardinia that I've seen before include "Adrian is seen in Mediterranean island" , "Island belonging to Italy" , "Island south of Corsica" , "Corsican neighbour" , "Large Italian island, capital Cagliari" .)