To pretend not to hear; to refuse to listen what could be unpleasant

You've been warned many times by your family and your friends that if you keep this up, you'll come to no good. Certainly, turning a deaf ear is of no help

Sei stato avvertito più volte dai tuoi familiari e dagli amici che se continui così, finirai male. Certo fare orecchi da mercante non ti aiuta

I'm talking to you and I know you are listening, so don't turn a deaf ear on me

Non fare orecchi da mercante! Sto parlando con te e so benissimo che mi stai ascoltando

When I bring up the subject about buying another car, my husband turns a deaf ear because he says we don't need a new one

Quando comincio a parlare di comperare un'altra macchina, mio marito fa orecchi da mercante perché dice che non ci serve una macchina nuova

The image of the ear turning suddenly deaf fits the situation so well, that it has been used since 1440, when Walter Hylthon wrote in Scala Perfeccionis:
"Make deef ere to hem as though thou herde haue not"