Drive out in attempt to cross North Island (6)
I believe the answer is:
banish
'drive out' is the definition.
(thesaurus)
'attempt to cross north island' is the wordplay.
'attempt' becomes 'bash' (I've seen this before).
'to cross' is an insertion indicator.
'north' becomes 'N' (synonyms).
'island' becomes 'i'.
'n'+'i'='ni'
'bash' placed around 'ni' is 'BANISH'.
'in' is the link.
(Other definitions for banish that I've seen before include "Condemn to exile" , "Expel or expatriate" , "Exile (someone)" , "Throw out" , "Exile in ash-bin" .)