You can certainly say that. People will have no trouble understanding you. Speaking as someone living in the U.S., I would not consider "get on with" to be a fixed idiom with a commonly agreed meaning. Rather, it is a flexible expression that means whatever it needs to mean in any sentence. For example, all of these make good sense: "Mary gets on well with Sally" ("along" would be better) "The lawyers have time now to get on with the contract" ("get going" would be better) "Their music is mostly bland. The band only really gets on with old-timey rock and roll" (It means they really come to life. This is not an established idiom, but the phrase "get on with" means almost anything the speaker wants it to mean) My personal choice would be not to use "getting on with" in the way you suggested. I would search for something more specific, like "How are you doing in your new job?" "How do you like your new job?" "How is your new job treating you?" (somewhat idiomatic) "Are you OK with your new job?" "Does your new job suit you (well)?" "Are you and your new job getting along?" (somewhat idiomatic) or "Are you getting along well in your new job" "Have you settled in with your new job?" Your Italian expression works well in English too. The only difference is that we would not use a reflexive verb: "How are you finding your new job?" (or "how do you find...") but you could: "How are you finding yourself in your new job?" My advice would be to stick with the Italian way. In my opinion, it's better to sound like an Italian speaking English than an Italian who wants to sound English. Your native expressions make you unique and special. Minimize your use of "get". It is the most overused word in the English language. Simultaneously, it means nothing and everything. It cannot be avoided, but the less, the better.

Hi Francesca! Yes, we would say that or “How’s it going with your new job?” I hope this helps!