To enable the advanced DNS options in cPanel, please do the following:

1. Log into WHM.
2. Go to Packages -> Feature Manager
3. Enter a feture name in the "Add new fetaure" section
4. Click "Add" to create the feature template.
5. The new list name will appear under the "Manage Features List" section.
6. Make sure it is selected in the dropdown and click the Edit button.
7. From here you will see a long lost of Features that are offered for accounts with this list. Select or Deselect the checkbox next to the Advanced DNS Zone Editor field along with any other features you require.
8. Scroll to the bottom and click on the Save button.
9. Then set the account in question to use the new feature.

You will now see the advanced DNS option under the account in cPanel. 

Alternatively, if the "Default" feature is the one that all accounts have been set up under then you can modify this one using the guide above from step 5. Simply select the "Default" feature list.