Letter from Greek island love cheers (4)
I believe the answer is:
iota
'letter from greek' is the definition.
(letter from the Greek alphabet)
'island love cheers' is the wordplay.
'island' becomes 'i' (geographical abbreviation).
'love' becomes 'o' (love means zero in tennis).
'cheers' becomes 'ta' (both can mean thank you).
'i'+'o'+'ta'='IOTA'
(Other definitions for iota that I've seen before include "Old letter" , "Greek letter - small quantity" , "Just a jot, from Greek alphabet" , "A little piece" , "Gr. letter; small amount" .)