diff --git a/.github/workflows/integration-test.yml b/.github/workflows/integration-test.yml
index 787e41aab..578674a77 100644
--- a/.github/workflows/integration-test.yml
+++ b/.github/workflows/integration-test.yml
@@ -84,7 +84,7 @@ jobs:
       - name: Add mock connectors
         working-directory: tests
         run: |
-          npm run cli connector add @logto/connector-mock-sms @logto/connector-mock-email @logto/connector-mock-social -- -p ../logto
+          npm run cli connector add @logto/connector-mock-sms @logto/connector-mock-email @logto/connector-mock-standard-email @logto/connector-mock-social -- -p ../logto
 
       - name: Run Logto
         working-directory: logto/
diff --git a/packages/integration-tests/src/__mocks__/connectors-mock.ts b/packages/integration-tests/src/__mocks__/connectors-mock.ts
index 049e65ea5..a27714899 100644
--- a/packages/integration-tests/src/__mocks__/connectors-mock.ts
+++ b/packages/integration-tests/src/__mocks__/connectors-mock.ts
@@ -140,6 +140,45 @@ export const mockEmailConnectorConfig = {
   ],
 };
 
+export const mockStandardEmailConnectorId = 'mock-standard-email-service';
+export const mockStandardEmailConnectorConfig = {
+  apiKey: 'api-key-value',
+  fromEmail: 'noreply@logto.test.io',
+  fromName: 'from-name-value',
+  templates: [
+    {
+      usageType: 'SignIn',
+      type: 'text/plain',
+      subject: 'Logto SignIn Template',
+      content: 'This is for sign-in purposes only. Your passcode is {{code}}.',
+    },
+    {
+      usageType: 'Register',
+      type: 'text/plain',
+      subject: 'Logto Register Template',
+      content: 'This is for registering purposes only. Your passcode is {{code}}.',
+    },
+    {
+      usageType: 'ForgotPassword',
+      type: 'text/plain',
+      subject: 'Logto Forgot Password Template',
+      content: 'This is for forgot-password purposes only. Your passcode is {{code}}.',
+    },
+    {
+      usageType: 'Continue',
+      type: 'text/plain',
+      subject: 'Logto Continue Template',
+      content: 'This is for completing user profile purposes only. Your passcode is {{code}}.',
+    },
+    {
+      usageType: 'Test',
+      type: 'text/plain',
+      subject: 'Logto Test Template',
+      content: 'This is for testing purposes only. Your passcode is {{code}}.',
+    },
+  ],
+};
+
 export const mockSocialConnectorId = 'mock-social-connector';
 export const mockSocialConnectorTarget = 'mock-social';
 export const mockSocialConnectorConfig = {
diff --git a/packages/integration-tests/tests/api/admin-user.test.ts b/packages/integration-tests/tests/api/admin-user.test.ts
index fbfd06b04..266ee2005 100644
--- a/packages/integration-tests/tests/api/admin-user.test.ts
+++ b/packages/integration-tests/tests/api/admin-user.test.ts
@@ -14,6 +14,7 @@ import {
   deleteUserIdentity,
   postConnector,
   updateConnectorConfig,
+  deleteConnectorById,
 } from '@/api';
 import { createUserByAdmin, bindSocialToNewCreatedUser } from '@/helpers';
 
@@ -81,5 +82,7 @@ describe('admin console user management', () => {
     const updatedUser = await getUser(createdUserId);
 
     expect(updatedUser.identities).not.toHaveProperty(mockSocialConnectorTarget);
+
+    await deleteConnectorById(id);
   });
 });
diff --git a/packages/integration-tests/tests/api/connector.test.ts b/packages/integration-tests/tests/api/connector.test.ts
index 9f777f8bc..ec5d65aca 100644
--- a/packages/integration-tests/tests/api/connector.test.ts
+++ b/packages/integration-tests/tests/api/connector.test.ts
@@ -7,6 +7,8 @@ import {
   mockSmsConnectorId,
   mockSocialConnectorConfig,
   mockSocialConnectorId,
+  mockStandardEmailConnectorConfig,
+  mockStandardEmailConnectorId,
 } from '@/__mocks__/connectors-mock';
 import {
   deleteConnectorById,
@@ -69,15 +71,29 @@ test('connector set-up flow', async () => {
   /*
    * Change to another SMS/Email connector
    */
-  // FIXME @Darcy [LOG-4750,4751]: complete this IT after add another mock sms/email connector (or other current existing connector could be affected)
+  const { id } = await postConnector(mockStandardEmailConnectorId);
+  await updateConnectorConfig(id, mockStandardEmailConnectorConfig);
+  connectorIdMap.set(mockStandardEmailConnectorId, id);
+  const currentConnectors = await listConnectors();
+  expect(
+    currentConnectors.some((connector) => connector.connectorId === mockEmailConnectorId)
+  ).toBeFalsy();
+  expect(
+    currentConnectors.some((connector) => connector.connectorId === mockStandardEmailConnectorId)
+  ).toBeTruthy();
+  expect(
+    currentConnectors.find((connector) => connector.connectorId === mockStandardEmailConnectorId)
+      ?.config
+  ).toEqual(mockStandardEmailConnectorConfig);
+  connectorIdMap.delete(mockEmailConnectorId);
 
   /*
    * Delete (i.e. disable) a connector
    */
   await expect(
-    deleteConnectorById(connectorIdMap.get(mockEmailConnectorId))
+    deleteConnectorById(connectorIdMap.get(mockStandardEmailConnectorId))
   ).resolves.not.toThrow();
-  connectorIdMap.delete(mockEmailConnectorId);
+  connectorIdMap.delete(mockStandardEmailConnectorId);
 
   /**
    * List connectors after manually setting up connectors.
@@ -130,4 +146,9 @@ test('send SMS/email test message', async () => {
   ).resolves.not.toThrow();
   await expect(sendSmsTestMessage(mockSmsConnectorId, phone, {})).rejects.toThrow(HTTPError);
   await expect(sendEmailTestMessage(mockEmailConnectorId, email, {})).rejects.toThrow(HTTPError);
+
+  for (const [_connectorId, id] of connectorIdMap.entries()) {
+    // eslint-disable-next-line no-await-in-loop
+    await deleteConnectorById(id);
+  }
 });
diff --git a/packages/integration-tests/tests/api/social-session.test.ts b/packages/integration-tests/tests/api/social-session.test.ts
index cacdde01c..4c5bf484b 100644
--- a/packages/integration-tests/tests/api/social-session.test.ts
+++ b/packages/integration-tests/tests/api/social-session.test.ts
@@ -15,6 +15,7 @@ import {
   getUser,
   postConnector,
   updateConnectorConfig,
+  deleteConnectorById,
 } from '@/api';
 import MockClient from '@/client';
 import { signUpIdentifiers } from '@/constants';
@@ -112,6 +113,13 @@ describe('social bind account', () => {
     await createUserByAdmin(username, password);
   });
 
+  afterAll(async () => {
+    for (const [_connectorId, id] of connectorIdMap.entries()) {
+      // eslint-disable-next-line no-await-in-loop
+      await deleteConnectorById(id);
+    }
+  });
+
   it('bind new social account', async () => {
     const client = new MockClient();