Irish backing singer in Venetian district (6)
I believe the answer is:
rialto
'venetian district' is the definition.
(area of Venice)
'irish backing singer' is the wordplay.
'irish' becomes 'IR' (abbreviation).
'backing' is a reversal indicator.
'singer' becomes 'alto' (alto is a kind of singer).
'ir' written backwards gives 'ri'.
'ri'+'alto'='RIALTO'
'in' acts as a link.
(Other definitions for rialto that I've seen before include "business centre" , "Venetian district" , "Venetian island" , "Famous Venetian bridge" , "Central area of Venice and suburb of Dublin" .)