Several contagious diseases can be spread between horses directly or via your hands, tack or equipment.
With this in mind, it is good practice to isolate and monitor any new horse that you introduce to your barn for 10 days to 3 weeks, long enough for you to discern any signs of illness.
What you can do in this instance depends in large part on the unique layout of your facility, how many horses you have on your property, where they are located, and the amount of help you have.
Ideally you should separate the new horse from others at a good distance (40 feet minimum) in a separate corral or barn. At minimum, you may isolate the new horse in an end stall and leave an empty stall between them and your other horses. Do not turn out the new horse with your other horses, or in a neighboring turnout until the quarantine period is over.
Depending on your level of concern, you can choose to treat the new horse as a contagious risk, and ensure that there is no direct or indirect contact with your other horses, via tack, equipment, buckets, other animals or you and your staff. Short of that, you may choose to simply prevent any direct contact with other horses and closely monitor the new horse during the quarantine period.
Tips for safety & Success
If the new horse shows any signs of illness, immediately contact your vet and consider increasing your efforts to ensure separation from your other horses by treating them as if they are contagious. Keep a close eye on your other horses.
Before the new horse arrives at your barn, ask for a valid health certificate (containing proof of a negative Coggins), and proof of recent vaccinations that are appropriate for your region. If a horse is arriving from far away, they may need to be vaccinated for diseases they were not previously exposed to, and you should discuss this with your vet. Inquire about the horse's health history, recent travel history and previous stabling.