Hello. I realize this is an old thread, but I found it searching for "Can a US vet practice in Europe" on google. The island of Vis, in Croatia, is a paradise, but lacks a vet, and I'm trying to find someone who might be interested in trying to set up a practice here.
So many things would have to be sorted out before this could happen. Just immediately off the top of my head:
What is Croatia's rules and laws on foreigners operating a business? Can they? What about owning land? Realty?
What is Croatia's rules and laws on foreigners practicing veterinary medicine in their country? Licenses? Pharmaceuticals access? Insurance - health/dental/life/malpractice?
Quality of life? Housing? What about children - schools? Cost of living? Expected pay and benefits?
What is Croatia's rules and laws as far as foreigners working in their country? Taxes? Licenses? By profession?
What is Croatia's rules and laws governing residency or even citizenship? Is dual citizenship even a thing granted by Croatia? Many Americans are not keen to renounce their US citizenship, even if expat and having to pay those associated taxes. Are there visa preferences by occupations that are hard to fill in your country like others? What about age restrictions? Heath restrictions?
What is Croatia's rules and laws as far as non-veterinarian having investment in a veterinary practice? There are states in the US where it is okay, others where possible only under specific circumstances/familial relationships, and states where it is illegal. I pose this one because who is going to set up a veterinary practice for this hypothetical veterinarian? Or do you expect someone to have the capital outlay just burning a hole in their pocket with a love of sandy beaches to waltz in and build as well as start up a ground up veterinary practice in a foreign country?
Species? If you are expecting mixed or large animal skills, you're search just became that much more of an up hill battle.
Emergency/critical care provision? What are the rules and laws governing? Here in the US if you can't refer it, you have to provide it. Good luck finding a solo doctor who is game as 3K people are plenty enough to keep him/her permanently sleep deprived trying to uphold that requirement if the same in Croatia.
Professional staff? Where's that going to come from? School educated technicians - don't see how any would just be hanging out in an area, waiting to be hired, with zero veterinary presence.
There are many rural areas in the US who would like a local veterinarian, too. They rarely get filled. I am sure the same applies across the globe. So what makes your tiny island the honey pot sweeter than anywhere else?
You could also look to countries who are actively doing what you are just in the dreaming stage of; see where they are at. What are they offering. If I am recollecting, correctly Guam is one example - that have or once upon a time had a deal where they had a clinic who advertised for something along the lines of 6 month/12 month temporary and/or rotating positions where they sponsored the doctor and did all the heavy lifting paperwork-wise to get the doctor on-island as well as provided housing.
Or even starting with your local veterinary medicine program. If you build it, they will come sort of thing. Whether as part of the school's curriculum as a teaching satellite facility or as a private/non-profit(?) entity. Whether as an occasional, but regular thing (e.g., clinics every two or four weeks), or a part-time position, or a full-time position.
Or contracting with a mainland veterinarian if you set up a plug-and-play sort of situation for them. Even if it's just for regular immunization clinics. Or surgical days. A lot of remote villages in places like Alaska do that. Contacting entities that set up such would give you more insight into how that works. RAVS is one US example of one that's for the poor/low income, but the organization is what you'd be interested in learning about vs. how to pay for it all -
HSVMA-RAVS: WELCOME.
Another option is to create a "home-grown" veterinarian where the island collectively advertises and grooms some local kid to complete their veterinary education and return for whatever minimum period of time under a contract. The theory behind this is it is for long enough that they settle down and will not want to leave the area once the contractual time has been fulfilled. You are, of course, back to building the practice for them, but it may be an option.
I am not trying to discourage you, but all that is just the tip of the proverbial iceberg. It isn't as simple as finding a doctor who'd move to Vis to turn your idea into reality. Hell, I'd probably move to Vis. But only if everything was on the up and up and just so and checked out after much scrutiny. Even then, to move there permanently? Probably not. That's not something any foreigner can determine until they've been somewhere, for some time.