diff --git a/changelogs/unreleased/4779-reasonerjt b/changelogs/unreleased/4779-reasonerjt
new file mode 100644
index 000000000..869257e84
--- /dev/null
+++ b/changelogs/unreleased/4779-reasonerjt
@@ -0,0 +1 @@
+Ensure the restore hook applied to new namespace based on the mapping
\ No newline at end of file
diff --git a/internal/hook/item_hook_handler.go b/internal/hook/item_hook_handler.go
index 5631b3359..96cb18bc6 100644
--- a/internal/hook/item_hook_handler.go
+++ b/internal/hook/item_hook_handler.go
@@ -104,6 +104,7 @@ func (i *InitContainerRestoreHookHandler) HandleRestoreHooks(
 	groupResource schema.GroupResource,
 	obj runtime.Unstructured,
 	resourceRestoreHooks []ResourceRestoreHook,
+	namespaceMapping map[string]string,
 ) (runtime.Unstructured, error) {
 	// We only support hooks on pods right now
 	if groupResource != kuberesource.Pods {
@@ -141,6 +142,13 @@ func (i *InitContainerRestoreHookHandler) HandleRestoreHooks(
 		namespace := metadata.GetNamespace()
 		labels := labels.Set(metadata.GetLabels())
 
+		// Apply the hook according to the target namespace in which the pod will be restored
+		// more details see https://github.com/vmware-tanzu/velero/issues/4720
+		if namespaceMapping != nil {
+			if n, ok := namespaceMapping[namespace]; ok {
+				namespace = n
+			}
+		}
 		for _, rh := range resourceRestoreHooks {
 			if !rh.Selector.applicableTo(groupResource, namespace, labels) {
 				continue
diff --git a/internal/hook/item_hook_handler_test.go b/internal/hook/item_hook_handler_test.go
index c1704d365..267c413a1 100644
--- a/internal/hook/item_hook_handler_test.go
+++ b/internal/hook/item_hook_handler_test.go
@@ -1395,11 +1395,12 @@ func TestGetRestoreHooksFromSpec(t *testing.T) {
 
 func TestHandleRestoreHooks(t *testing.T) {
 	testCases := []struct {
-		name          string
-		podInput      corev1api.Pod
-		restoreHooks  []ResourceRestoreHook
-		expectedPod   *corev1api.Pod
-		expectedError error
+		name             string
+		podInput         corev1api.Pod
+		restoreHooks     []ResourceRestoreHook
+		namespaceMapping map[string]string
+		expectedPod      *corev1api.Pod
+		expectedError    error
 	}{
 		{
 			name: "should handle hook from annotation no hooks in spec on pod with no init containers",
@@ -1840,6 +1841,87 @@ func TestHandleRestoreHooks(t *testing.T) {
 			},
 			restoreHooks: []ResourceRestoreHook{},
 		},
+		{
+			name: "should not apply init container when the namespace mapping is provided and the hook points to the original namespace",
+			podInput: corev1api.Pod{
+				ObjectMeta: metav1.ObjectMeta{
+					Name:      "app1",
+					Namespace: "default",
+				},
+				Spec: corev1api.PodSpec{},
+			},
+			expectedError: nil,
+			expectedPod: &corev1api.Pod{
+				ObjectMeta: metav1.ObjectMeta{
+					Name:      "app1",
+					Namespace: "default",
+				},
+				Spec: corev1api.PodSpec{},
+			},
+			restoreHooks: []ResourceRestoreHook{
+				{
+					Name: "hook1",
+					Selector: ResourceHookSelector{
+						Namespaces: collections.NewIncludesExcludes().Includes("default"),
+						Resources:  collections.NewIncludesExcludes().Includes(kuberesource.Pods.Resource),
+					},
+					RestoreHooks: []velerov1api.RestoreResourceHook{
+						{
+							Init: &velerov1api.InitRestoreHook{
+								InitContainers: []corev1api.Container{
+									*builder.ForContainer("restore-init-container-1", "nginx").
+										Command([]string{"a", "b", "c"}).Result(),
+								},
+							},
+						},
+					},
+				},
+			},
+			namespaceMapping: map[string]string{"default": "new"},
+		},
+		{
+			name: "should apply init container when the namespace mapping is provided and the hook points to the new namespace",
+			podInput: corev1api.Pod{
+				ObjectMeta: metav1.ObjectMeta{
+					Name:      "app1",
+					Namespace: "default",
+				},
+				Spec: corev1api.PodSpec{},
+			},
+			expectedError: nil,
+			expectedPod: &corev1api.Pod{
+				ObjectMeta: metav1.ObjectMeta{
+					Name:      "app1",
+					Namespace: "default",
+				},
+				Spec: corev1api.PodSpec{
+					InitContainers: []corev1api.Container{
+						*builder.ForContainer("restore-init-container-1", "nginx").
+							Command([]string{"a", "b", "c"}).Result(),
+					},
+				},
+			},
+			restoreHooks: []ResourceRestoreHook{
+				{
+					Name: "hook1",
+					Selector: ResourceHookSelector{
+						Namespaces: collections.NewIncludesExcludes().Includes("new"),
+						Resources:  collections.NewIncludesExcludes().Includes(kuberesource.Pods.Resource),
+					},
+					RestoreHooks: []velerov1api.RestoreResourceHook{
+						{
+							Init: &velerov1api.InitRestoreHook{
+								InitContainers: []corev1api.Container{
+									*builder.ForContainer("restore-init-container-1", "nginx").
+										Command([]string{"a", "b", "c"}).Result(),
+								},
+							},
+						},
+					},
+				},
+			},
+			namespaceMapping: map[string]string{"default": "new"},
+		},
 	}
 
 	for _, tc := range testCases {
@@ -1847,7 +1929,7 @@ func TestHandleRestoreHooks(t *testing.T) {
 			handler := InitContainerRestoreHookHandler{}
 			podMap, err := runtime.DefaultUnstructuredConverter.ToUnstructured(&tc.podInput)
 			assert.NoError(t, err)
-			actual, err := handler.HandleRestoreHooks(velerotest.NewLogger(), kuberesource.Pods, &unstructured.Unstructured{Object: podMap}, tc.restoreHooks)
+			actual, err := handler.HandleRestoreHooks(velerotest.NewLogger(), kuberesource.Pods, &unstructured.Unstructured{Object: podMap}, tc.restoreHooks, tc.namespaceMapping)
 			assert.Equal(t, tc.expectedError, err)
 			actualPod := new(corev1api.Pod)
 			err = runtime.DefaultUnstructuredConverter.FromUnstructured(actual.UnstructuredContent(), actualPod)
diff --git a/pkg/restore/init_restorehook_pod_action.go b/pkg/restore/init_restorehook_pod_action.go
index e9cd33d35..f994d811d 100644
--- a/pkg/restore/init_restorehook_pod_action.go
+++ b/pkg/restore/init_restorehook_pod_action.go
@@ -49,11 +49,12 @@ func (a *InitRestoreHookPodAction) Execute(input *velero.RestoreItemActionExecut
 	a.logger.Infof("Executing InitRestoreHookPodAction")
 	// handle any init container restore hooks for the pod
 	restoreHooks, err := hook.GetRestoreHooksFromSpec(&input.Restore.Spec.Hooks)
+	nsMapping := input.Restore.Spec.NamespaceMapping
 	if err != nil {
 		return nil, errors.WithStack(err)
 	}
 	hookHandler := hook.InitContainerRestoreHookHandler{}
-	postHooksItem, err := hookHandler.HandleRestoreHooks(a.logger, kuberesource.Pods, input.Item, restoreHooks)
+	postHooksItem, err := hookHandler.HandleRestoreHooks(a.logger, kuberesource.Pods, input.Item, restoreHooks, nsMapping)
 	if err != nil {
 		return nil, errors.WithStack(err)
 	}