diff --git a/tests/cypress.json b/tests/cypress.json
index fe266d54eba75e89ea2095fce1d8dd52d0db6645..1588e3cefaa627d5d24f143c9387317070048306 100644
--- a/tests/cypress.json
+++ b/tests/cypress.json
@@ -11,7 +11,7 @@
   },
   "testFiles": [
     "auth_page.js",
-    "actions_tasks_objects/*",
+    "actions_tasks_objects/**/*",
     "actions_users/**/*",
     "actions_projects/**/*",
     "remove_users_tasks_projects.js"
diff --git a/tests/cypress/integration/actions_tasks_objects/registration_involved/case_39_issue_2572_rename_task.js b/tests/cypress/integration/actions_tasks_objects/registration_involved/case_39_issue_2572_rename_task.js
new file mode 100644
index 0000000000000000000000000000000000000000..f21c65ec19aeef6cc1e0999519573d25e57922cc
--- /dev/null
+++ b/tests/cypress/integration/actions_tasks_objects/registration_involved/case_39_issue_2572_rename_task.js
@@ -0,0 +1,78 @@
+// Copyright (C) 2021 Intel Corporation
+//
+// SPDX-License-Identifier: MIT
+
+/// <reference types="cypress" />
+
+context('Rename a task.', () => {
+    const caseId = '39';
+    const labelName = `Case ${caseId}`;
+    const taskName = `New annotation task for ${labelName}`;
+    const attrName = `Attr for ${labelName}`;
+    const textDefaultValue = 'Some default value for type Text';
+    const imagesCount = 1;
+    const imageFileName = `image_${labelName.replace(' ', '_').toLowerCase()}`;
+    const width = 800;
+    const height = 800;
+    const posX = 10;
+    const posY = 10;
+    const color = 'gray';
+    const archiveName = `${imageFileName}.zip`;
+    const archivePath = `cypress/fixtures/${archiveName}`;
+    const imagesFolder = `cypress/fixtures/${imageFileName}`;
+    const directoryToArchive = imagesFolder;
+    const newNaskName = taskName.replace('39', '3339');
+    const secondUserName = 'Case39';
+    const secondUser = {
+        firstName: `Firtstnamerenametask`,
+        lastName: `Lastnamerenametask`,
+        emailAddr: `${secondUserName.toLowerCase()}@local.local`,
+        password: 'Pass!UserCase39',
+    };
+
+    function renameTask(taskName, newValue) {
+        cy.get('.cvat-task-details-task-name').within(() => {
+            cy.get('[aria-label="edit"]').click();
+        });
+        cy.contains('.cvat-text-color', taskName).click().type(newValue);
+    }
+
+    before(() => {
+        cy.visit('auth/login');
+        cy.login();
+        cy.imageGenerator(imagesFolder, imageFileName, width, height, color, posX, posY, labelName, imagesCount);
+        cy.createZipArchive(directoryToArchive, archivePath);
+        cy.createAnnotationTask(taskName, labelName, attrName, textDefaultValue, archiveName);
+        cy.openTask(taskName);
+    });
+
+    after(() => {
+        cy.login();
+        cy.getTaskID(newNaskName).then(($taskID) => {
+            cy.deleteTask(newNaskName, $taskID);
+        });
+    });
+
+    describe(`Testing "${labelName}". Issue 2572.`, () => {
+        it('Rename the task. Issue is not reproduce.', () => {
+            renameTask(taskName, '{leftarrow}{leftarrow}33{Enter}');
+            cy.contains('.cvat-task-details-task-name', newNaskName).should('exist');
+            cy.logout();
+        });
+        it('Registration a second user. Rename the task. Status 403 appear.', () => {
+            cy.goToRegisterPage();
+            cy.userRegistration(
+                secondUser.firstName,
+                secondUser.lastName,
+                secondUserName,
+                secondUser.emailAddr,
+                secondUser.password,
+            );
+            cy.openTask(newNaskName);
+            renameTask(newNaskName, '{leftarrow}{leftarrow}3{Enter}');
+            cy.get('.cvat-notification-notice-update-task-failed').should('exist');
+            cy.closeNotification('.cvat-notification-notice-update-task-failed');
+            cy.logout(secondUserName);
+        });
+    });
+});