Async support comes in 2 flavors: you can return a CompletionStage or a Uni (requires the quarkus-rest-client-mutiny extension).

package org.acme.rest.client;

import org.eclipse.microprofile.rest.client.inject.RegisterRestClient;
import org.jboss.resteasy.annotations.jaxrs.PathParam;

import javax.ws.rs.GET;
import javax.ws.rs.Path;
import javax.ws.rs.Produces;
import java.util.concurrent.CompletionStage;
import java.util.Set;

@Path("/v2")
@RegisterRestClient
public interface CountriesService {

    // ...

    @GET
    @Path("/name/{name}")
    @Produces("application/json")
    Uni<Set<Country>> getByNameAsUni(@PathParam String name);
}

package org.acme.rest.client;

import org.eclipse.microprofile.rest.client.inject.RestClient;
import org.jboss.resteasy.annotations.jaxrs.PathParam;

import javax.inject.Inject;
import javax.ws.rs.GET;
import javax.ws.rs.Path;
import javax.ws.rs.Produces;
import javax.ws.rs.core.MediaType;
import java.util.concurrent.CompletionStage;
import java.util.Set;

@Path("/country")
public class CountriesResource {

    @Inject
    @RestClient
    CountriesService countriesService;


    // ...

    @GET
    @Path("/name-uni/{name}")
    public Uni<Set<Country>> nameAsync(@PathParam String name) {
        return countriesService.getByNameAsUni(name);
    }
}