Passport and Visa are two different things. Getting a new passport doesn't tamper you identity. Visa with a new passport is allowed.
-> Do carry the old passport when you travel...
-> it sometimes differ from the countries, so you may get an authorization letter requesting the passport authority for more legal backup.....
-> you may send a new passport details and you present visa details to the department which has issued your visa for there consideration as an update........ you also request there reply so that you may carry it while traveling...
-> you may crosscheck with the authority is they have the provision to issue new visa accordingly.........
You may refer these websites for more info......
UAE Visas | Visa & Passport Information | Emirates
Visas & Passports for Travel to the UAE | UAE Embassy in Washington, DC