Realm has a rather clever internal caching system where previous instances of Realm are held onto and recycled each time a call like let realm = try! Realm() occurs. As such, it's not really necessary, nor recommended to try and incorporate a Realm instance itself into a singleton.
If you want to heavily customise your Realm instance's settings, you'll normally do that through a Realm Configuration object, which is static and thread-safe. If that's the case, it would be more appropriate to have a singleton (or even just a static class method) that returns the appropriate Configuration object when you need to create a new Realm instance.
that thing in swift has a page on how to create singletons in Swift, and it's essentially just a single static property of a class implementation:
class SomeManager {
    static let sharedInstance = SomeManager()
}