As far as I know, there is no task approval feature until Odoo Version 14. Therefore, you may need Customization Work here. It may not  be possible for a non-technical user to do Customization Work. Therefore, it is better to use Odoo Service or Odoo Partner Service. 

Hi,

I think for this you can create a record rule like this,

<record id="id_for_the_rule" model="ir.rule">	
    <field name="name">Task Visibility</field>	
    <field ref="model_project_task" name="model_id"/>	
    <field name="domain_force">[('state', '=', 'state_name')]</field>	
    <field name="groups" eval="[(4, ref('user_group_name'))]"/>
</record>

This will make the users to view the task only in approved state.

Thanks