RXJS Emit first result and then wait for another observable

You need to merge your observables together :

let obs = Observable.fromPromise(this.clientService.getClients())
      .map((clients) => {
        return clients.map((c) => new Client().fromObject(c));
      }).share();

let filtered = obs.switchMap((values) => {
    return this.searchText.valueChanges
        .debounceTime(400)
        .distinctUntilChanged()
        .map((text) => {
        return values.filter((c) => c.isMatch(text));
        });
    });

this.clients = Observable.merge(obs,filtered);

first you need to use the share operator to avoid fetching clients twice (see edit further). then you need to get the value from obs and also from filtered. this is what merge is made for :

Creates an output Observable which concurrently emits all values from every given input Observable.

Flattens multiple Observables together by blending their values into one Observable.

[source]

Edit : The share part is not necessary in this specific case as the OP is using a promise as observable source, promises not being triggered by the subscription, they are hot observables and do not need to be shared. But if you are dealing with other observable source (like angular Http service's method, you might need to share.