Republic's island in hot current (5)
I believe the answer is:
haiti
'republic's' is the definition.
(I've seen this before)
'island in hot current' is the wordplay.
'island' becomes 'ait' (term for a small island).
'in' means one lot of letters goes inside another.
'hot' becomes 'h' (abbreviation eg on taps).
'current' becomes 'I' (physics symbol).
'h'+'i'='hi'
'ait' going into 'hi' is 'HAITI'.
(Other definitions for haiti that I've seen before include "Western half of Hispaniola" , "West Indian republic" , "Republic sharing WI isle" , "W. Indies republic on Hispaniola" , "Country in W Indies, capital Port-au-Prince" .)