Clue: Run around collecting gold somewhere near Hawaii (5)
Answer: NAURU
Explanation: Definition: somewhere near Hawaii
An envelope ('collecting') of AU (chemical symbol, 'gold') in NRU, an anagram ('around') of 'run'. 'Somewhere near Hawaii'? – there's a fair swath of Pacific Ocean between them. It might not be quite like saying that Nauru, Tanzania is somewhere near London, but not that much different.