Caveat: I am not a vet, nor do I in any way, shape, or form have any inside information. I'm just a customer. But because I have a lot of mutts and spend a great deal of time seeking veterinary care, I've met, and chatted with, a lot of vets.
Throughout the years we've been treated by several Italian-educated vets; I would guess finding work here likely boils down to your qualifications (and getting them recognized) your area of specialization, your language skills, your experience to date - and your network.
The Italian vets I've met were working at the Tierspital (Uni ZH) pursuing further specialization, at the AOIC (oncology specialist center) on an educational exchange, as outside specialists partnering with private practices, in the practice that serves as the area 24/7 ER, and as general vets in private practice.
FYI, of the many vets I have seen over the years I'd say at least half are not Swiss.
So the question for you to focus on - what do you bring with you that would be of interest to a Swiss practice? Concentrate on that.
As you no doubt know, language and communication skills are paramount in veterinary medicine. Your clients, the owners, want to speak in the language they are most comfortable in. For instance, although I speak German I insist on speaking English with my vets, to do the best for my dogs I must ensure that there is little chance for misunderstanding. Most of the vets I have met are multi-lingual for that very reason - it's good business.
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A veterinary nurse in the UK sense might be a bit different, but would likelyfall under TPA, Tierpraxisassistant. If I understand the system correctly, one can specialize or seek further qualifications as well. You can read up about what a TPA does here, see how closely this aligns with your education and experience: (In German and French.)
https://www.gstsvs.ch/de/tiermedizin...entin-tpa.html
By the way, the GSTSVS site would also have contacts/relevant information for your partner.
(I don't know any Italian, so I've used the German terms.)