Define a one-to-many dependency between objects so that when one object changes state, all its dependents are notified and updated automatically.
That intent is actual very straight forward, put another way, when the state of A updates, the state of B should update to.
Clojure has several stateful abstractions built in that handle concurrency issues so you don't have to. Lets use a helpful chart to pick the right one:
Look at all the questions you need to answer in order to adequately handle real state coordination. None of which are address in the observer pattern.
I create a toy example and choose an abstraction based on that, but it would be pedantic.
Different ways of creating Observers are built into Clojure.