diff --git a/tests/prometheus/prometheus.yaml b/tests/prometheus/prometheus.yaml
index a019b61ac8bf169c433bb950d0abc5132d6eab2e..e10f24abad215773ba0d109b09e2ff8db94dbb5c 100644
--- a/tests/prometheus/prometheus.yaml
+++ b/tests/prometheus/prometheus.yaml
@@ -21,7 +21,7 @@ tests:
           apiVersion: "monitoring.coreos.com/v1"
           name: it-monit-metrics-collector-prometheus
         not: true
-  - it: should be deployed with cluster-local remote write by default
+  - it: should be deployed with cluster-local remote write by default and k8s_cluster_name set
     set:
       kubernetes.clusterName: test
     asserts:
@@ -35,6 +35,9 @@ tests:
       - equal:
           path: spec.remoteWrite[0].url
           value: "http://it-monit-metrics-fluentbit:8080/api/prom/push"
+      - equal:
+          path: spec.externalLabels.k8s_cluster_name
+          value: test
   - it: should be deployed with no remoteWrites if no fluentbit is available
     set:
       kubernetes.clusterName: test
@@ -47,7 +50,7 @@ tests:
       - lengthEqual:
           path: spec.remoteWrite
           count: 0
-  - it: should be deployed with external remote write if configured
+  - it: should be deployed with external remote write if configured and no external labels
     set:
       kubernetes.clusterName: test
       metrics.fluentbit.enabled: false
@@ -70,6 +73,8 @@ tests:
               password:
                 name: it-monit-metrics-collector-prometheus
                 key: password
+      - isNullOrEmpty:
+          path: spec.externalLabels
       - lengthEqual:
           path: spec.remoteWrite
           count: 1