Put up Irish singer in district of Venice (6)
I believe the answer is:
rialto
'district of venice' is the definition.
(I've seen this before)
'put up irish singer' is the wordplay.
'put up' says the letters should be written in reverse.
'irish' becomes 'ir' (abbreviation).
'singer' becomes 'alto' (alto is a kind of singer**).
'ir' in reverse letter order is 'ri'.
'ri'+'alto'='RIALTO'
'in' is the link.
(Other definitions for rialto that I've seen before include "Region in Venice and Dublin" , "Old mercantile area of Venice" , "Famous Venetian bridge" , "Area famous for 7 [ABRIDGE]" , "Dublin district, or Shakespeare's 'What news on the . . . . . .?'" .)