First of all, our adventurer happening upon a Pacific island (4)
I believe the answer is:
oahu
'a pacific island' is the definition.
(I've seen this before)
'first of all our adventurer happening upon' is the wordplay.
'first of all' indicates taking the first letters.
The first letters of 'our adventurer happening upon' is 'OAHU'.
(Other definitions for oahu that I've seen before include "Pacific island" , "Chief island of Hawaii" , "Hawaiian island" , "Honolulu's island" , "popular Pacific location" .)