Cheers affected one island (6)
I believe the answer is:
tahiti
'island' is the definition.
(I know that Tahiti is a island)
'cheers affected one' is the wordplay.
'cheers' becomes 'ta' (both can mean thank you).
'affected' becomes 'hit' (I've seen this in another clue).
'one' becomes 'i' (Roman numeral).
'ta'+'hit'+'i'='TAHITI'
(Other definitions for tahiti that I've seen before include "Society member" , "South Pacific island where both Robert Louis Stevenson and Paul Gauguin spent time" , "One of the Society Islands" , "Pacific island, Gauguin's home in the 1890s" , "French Polynesian island" .)