You need the following permissions assigned to employees' role or post, in this instance, as this permission is going to apply for all employees, this can be assigned to the employee role.
Permissions required
Menu MyDetails - with view and edit access
My Details: Contact Details - with view, edit, and add access
Assign permissions steps
To apply this to the employee role, you need to follow the below steps:
Click Admin Menu or Configuration.
Click Roles and Permissions.
Click the Employee role then click Edit.
Assign the above permissions to the employee role then click Save.