Clue: Irish backed singer in Italian island (6)
Answer: RIALTO
Explanation: Definition: Italian island
**<=Ir.** (Irish, *backed*) + **ALTO** ("singer") 
I don't think Rialto is an island per se; it is **part of** one of the islands that make up Venice, so saying it is an island is a bit like saying Scotland is an island. (see comments below)