Advance after crossing island (5)
I believe the answer is:
posit
'advance' is the definition.
(both can mean to put forward or suggest)
'after crossing island' is the wordplay.
'after' becomes 'post' (prefix meaning after, eg post-war).
'crossing' is an insertion indicator (to cross can mean to go over or around).
'island' becomes 'i' (geographical abbreviation).
'post' going around 'i' is 'POSIT'.
(Other definitions for posit that I've seen before include "Assume something as a basis for discussion" , "Put forward (something) as a given" , "Suggest" , "Put forward as true" , "Put forward; place" .)