diff --git a/pkg/app/sleep.go b/pkg/app/sleep.go
index 9f4d21c5..01447bd6 100644
--- a/pkg/app/sleep.go
+++ b/pkg/app/sleep.go
@@ -26,9 +26,12 @@ import (
 )
 
 type sleep struct {
-	ns            string
-	injectSidecar bool
-	tproxy        bool
+	ns              string
+	injectSidecar   bool
+	tproxy          bool
+	securityContext bool
+	runAsUser       int
+	runAsGroup      int
 }
 
 var _ App = &sleep{}
@@ -45,6 +48,16 @@ func SleepTroxy(ns string) App {
 	return &sleep{ns: ns, injectSidecar: true, tproxy: true}
 }
 
+func SleepSecurityContext(ns string, uid, gid int) App {
+	return &sleep{
+		ns:              ns,
+		injectSidecar:   true,
+		securityContext: true,
+		runAsUser:       uid,
+		runAsGroup:      gid,
+	}
+}
+
 func (a *sleep) Name() string {
 	return "sleep"
 }
@@ -66,10 +79,14 @@ func (a *sleep) Uninstall(t test.TestHelper) {
 func (a *sleep) values(t test.TestHelper) map[string]interface{} {
 	proxy := oc.GetProxy(t)
 	return map[string]interface{}{
-		"InjectSidecar": a.injectSidecar,
-		"HttpProxy":     proxy.HTTPProxy,
-		"HttpsProxy":    proxy.HTTPSProxy,
-		"NoProxy":       proxy.NoProxy,
+		"InjectSidecar":   a.injectSidecar,
+		"HttpProxy":       proxy.HTTPProxy,
+		"HttpsProxy":      proxy.HTTPSProxy,
+		"NoProxy":         proxy.NoProxy,
+		"Tproxy":          a.tproxy,
+		"securityContext": a.securityContext,
+		"runAsUser":       a.runAsUser,
+		"runAsGroup":      a.runAsGroup,
 	}
 }
 
@@ -204,6 +221,11 @@ spec:
         volumeMounts:
         - mountPath: /etc/sleep/tls
           name: secret-volume
+        {{ if .securityContext }}
+        securityContext:
+          runAsUser: {{ .runAsUser }}
+          runAsGroup: {{ .runAsGroup }}
+        {{ end }}
       volumes:
       - name: secret-volume
         secret:
diff --git a/pkg/tests/ossm/privileged_pods_test.go b/pkg/tests/ossm/privileged_pods_test.go
new file mode 100644
index 00000000..ec609f4b
--- /dev/null
+++ b/pkg/tests/ossm/privileged_pods_test.go
@@ -0,0 +1,93 @@
+// Copyright 2024 Red Hat, Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//	http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package ossm
+
+import (
+	"testing"
+
+	"github.com/maistra/maistra-test-tool/pkg/app"
+	"github.com/maistra/maistra-test-tool/pkg/util/check/assert"
+	"github.com/maistra/maistra-test-tool/pkg/util/env"
+	"github.com/maistra/maistra-test-tool/pkg/util/ns"
+	"github.com/maistra/maistra-test-tool/pkg/util/oc"
+	"github.com/maistra/maistra-test-tool/pkg/util/pod"
+	"github.com/maistra/maistra-test-tool/pkg/util/shell"
+	"github.com/maistra/maistra-test-tool/pkg/util/version"
+
+	. "github.com/maistra/maistra-test-tool/pkg/util/test"
+)
+
+func TestInjectionInPrivelegedPods(t *testing.T) {
+	NewTest(t).Groups(Full, Disconnected, ARM).Run(func(t TestHelper) {
+		if env.GetOperatorVersion().LessThan(version.OPERATOR_2_6_2) {
+			t.Skip("This test requires the operator version to be at least 2.6.2")
+		}
+		t.Log("Reference: https://issues.redhat.com/browse/OSSM-8001")
+
+		t.Cleanup(func() {
+			app.Uninstall(t, app.Httpbin(ns.Foo))
+			oc.RecreateNamespace(t, meshNamespace)
+		})
+
+		t.LogStep("Deploy smcp")
+		DeployControlPlane(t)
+
+		t.LogStep("Patch SMCP to enable mTLS in dataPlane and controlPlane")
+		oc.Patch(t, meshNamespace, "smcp", smcpName, "merge", `
+spec:
+  security:
+    dataPlane:
+      mtls: true
+    controlPlane:
+      mtls: true
+`)
+
+		t.LogStep("Deploy httpbin")
+		app.InstallAndWaitReady(t, app.Httpbin(ns.Foo))
+
+		t.NewSubTest("Check sleep with explicitly defined SecurityContext with same uid/gid (1001)").Run(func(t TestHelper) {
+			runSecurityContextTest(t, 1001, 1001, "uid=1002(1002) gid=1002 groups=1002")
+		})
+
+		t.NewSubTest("Check sleep with explicitly defined SecurityContext with root uid/gid").Run(func(t TestHelper) {
+			runSecurityContextTest(t, 0, 0, "uid=1(bin) gid=1(bin) groups=1(bin)")
+		})
+	})
+}
+
+func runSecurityContextTest(t TestHelper, uid, gid int, expectedIDOutput string) {
+	t.Cleanup(func() {
+		app.Uninstall(t, app.SleepSecurityContext(ns.Foo, uid, gid))
+	})
+
+	t.LogStep("Provide privileged policy to sleep SA")
+	shell.Execute(t, "oc adm policy add-scc-to-user privileged -z sleep -n foo")
+
+	t.LogStep("Deploy sleep")
+	app.InstallAndWaitReady(t,
+		app.SleepSecurityContext(ns.Foo, uid, gid),
+	)
+
+	t.LogStepf("Verify that UID, GID and Groups were changed to: %s", expectedIDOutput)
+	oc.Exec(t, pod.MatchingSelector("app=sleep", ns.Foo), "istio-proxy",
+		"id",
+		assert.OutputContains(
+			expectedIDOutput,
+			"UID, GID and Groups were changed",
+			"UID, GID and Groups were not changed"))
+
+	t.LogStep("Verify that a request from sleep to httpbin returns 200")
+	app.AssertSleepPodRequestSuccess(t, ns.Foo, "http://httpbin:8000/ip")
+}
diff --git a/pkg/util/version/operator_version.go b/pkg/util/version/operator_version.go
index a43ee3e0..11760f4e 100644
--- a/pkg/util/version/operator_version.go
+++ b/pkg/util/version/operator_version.go
@@ -17,4 +17,5 @@ package version
 var (
 	OPERATOR_2_5_2 = ParseVersion("2.5.2")
 	OPERATOR_2_6_0 = ParseVersion("2.6.0")
+	OPERATOR_2_6_2 = ParseVersion("2.6.2")
 )