Mystery mage swimming round North Island (6)
I believe the answer is:
enigma
'mystery' is the definition.
(synonyms)
'mage swimming round north island' is the wordplay.
'swimming' is an anagram indicator (letters swim around into a new order).
'round' is an insertion indicator.
'north' becomes 'N' (abbreviation).
'island' becomes 'i' (geographical abbreviation).
'mage' is an anagram of 'egma'.
'n'+'i'='ni'
'egma' placed around 'ni' is 'ENIGMA'.
(Other definitions for enigma that I've seen before include "WWII cipher" , "It's mysterious like gamine" , "Riddle - German coding machine" , "'Puzzle, riddle (6)'" , "Puzzle for gaming" .)