Island where a dollar cut up (4)
I believe the answer is:
cuba
'island' is the definition.
(Cuba is an example)
'a dollar cut up' is the wordplay.
'dollar' becomes 'buck' (slang).
'cut' means to remove the last letter.
'up' is a reversal indicator (in down clue: letters go upwards).
'a'+'buck'='abuck'
'abuck' with its last letter taken away is 'abuc'.
'abuc' written backwards gives 'CUBA'.
'where' is the link.
(Other definitions for cuba that I've seen before include "Island S. of Florida" , "West Indian island" , "tropical country" , "Country famous for its cigars" , "Island nation" .)