Infidel quietly once more abandoning island (5)
I believe the answer is:
pagan
'infidel' is the definition.
(synonyms)
'quietly once more abandoning island' is the wordplay.
'quietly' becomes 'p' (p for piano and quiet).
'once more' becomes 'again' (synonyms).
'abandoning' indicates named letters should be taken away.
'island' becomes 'i' (geographical abbreviation).
'again' with 'i' taken away is 'agan'.
'p'+'agan'='PAGAN'
(Other definitions for pagan that I've seen before include "One who does not acknowledge your god(s)" , "One outside the main religions" , "A heathen, not a Christian" , "advocate of pleasures" , "Unchristian" .)