diff --git a/spec/jobs/nbp_sync_job_spec.rb b/spec/jobs/nbp_sync_job_spec.rb
new file mode 100644
index 000000000..4b89f7129
--- /dev/null
+++ b/spec/jobs/nbp_sync_job_spec.rb
@@ -0,0 +1,45 @@
+# frozen_string_literal: true
+
+require 'rails_helper'
+
+RSpec.describe NbpSyncJob do
+  let(:task) { create(:task, access_level:) }
+  let(:uuid) { task.uuid }
+
+  before do
+    allow(Nbp::PushConnector).to receive(:instance)
+    allow(Nbp::PushConnector.instance).to receive(:push_lom!)
+    allow(Nbp::PushConnector.instance).to receive(:delete_task!)
+  end
+
+  describe 'perform' do
+    subject(:perform_job) { described_class.perform_now(uuid) }
+
+    context 'when the task is public' do
+      let(:access_level) { :public }
+
+      it 'pushes the task' do
+        perform_job
+        expect(Nbp::PushConnector.instance).to have_received(:push_lom!)
+      end
+    end
+
+    context 'when the task does not exist' do
+      let(:uuid) { :not_existing_uuid }
+
+      it 'deletes the task' do
+        perform_job
+        expect(Nbp::PushConnector.instance).to have_received(:delete_task!)
+      end
+    end
+
+    context 'when the task is private' do
+      let(:access_level) { :private }
+
+      it 'deletes the task' do
+        perform_job
+        expect(Nbp::PushConnector.instance).to have_received(:delete_task!)
+      end
+    end
+  end
+end
diff --git a/spec/lib/nbp/push_connector_spec.rb b/spec/lib/nbp/push_connector_spec.rb
index beca53fec..decbb2bfe 100644
--- a/spec/lib/nbp/push_connector_spec.rb
+++ b/spec/lib/nbp/push_connector_spec.rb
@@ -15,15 +15,14 @@
     stub_request(:post, Settings.nbp.push_connector.token_path).to_return_json(body: {token: 'sometoken', expires_in: 600})
     stub_request(:post, "#{api_host}/datenraum/api/core/sources")
     stub_request(:put, "#{api_host}/push-connector/api/lom-v2/#{source_slug}")
+    stub_request(:delete, %r{#{api_host}/push-connector/api/course/#{source_slug}/})
     stub_request(:get, "#{api_host}/datenraum/api/core/sources/slug/#{source_slug}").to_return(status: 404)
   end
 
-  describe 'push_lom!' do
-    subject(:push_lom!) { connector.push_lom!(task_xml) }
-
+  describe 'initialize' do
     context 'when no source exists' do
       it 'creates a source' do
-        push_lom!
+        connector
         expect(WebMock).to have_requested(:post, "#{api_host}/datenraum/api/core/sources")
       end
     end
@@ -32,10 +31,14 @@
       before { stub_request(:get, "#{api_host}/datenraum/api/core/sources/slug/#{source_slug}").to_return(status: 200) }
 
       it 'does not create a source' do
-        push_lom!
+        connector
         expect(WebMock).not_to have_requested(:post, "#{api_host}/datenraum/api/core/sources")
       end
     end
+  end
+
+  describe 'push_lom!' do
+    subject(:push_lom!) { connector.push_lom!(task_xml) }
 
     context 'without any errors' do
       it 'pushes the metadata' do
@@ -44,4 +47,15 @@
       end
     end
   end
+
+  describe 'delete_task!' do
+    subject(:delete_task!) { connector.delete_task!(task.uuid) }
+
+    context 'without any errors' do
+      it 'pushes the metadata' do
+        delete_task!
+        expect(WebMock).to have_requested(:delete, "#{api_host}/push-connector/api/course/#{source_slug}/#{task.uuid}")
+      end
+    end
+  end
 end