Hi Melis,
Sorry for the delayed reply. Please note that this depends on whether you are using a modern site or a classic site.
This is how a modern site looks like:
This is how a classic site looks like:
You may check this article for more details.
If you are using a modern site, then I'm sorry to inform you that task list isn't an available web part in a modern site yet. You may check the detailed list of the available web parts in a modern site from here. I would recommend that you post your suggestion in the SharePoint Administration forum in UserVoice or vote for this feature in this thread Need to add Task list to SharePoint Modern experience so that our SharePoint development team could know your needs and add this new feature to the modern experience in the future.
As a work around, you may try adding your task list in the left navigation panel to enable your users to notice and access your task list easily. Please refer to the following steps:
1.Open your task list in Site Content and copy the URL of the task list;
2.Go back to the site page and click Edit in the left navigation panel;
3.Move the cursor to the navigation list and click "+" to add a new item;
4.Paste the URL into "Address", add a display name and click OK.
If you are using a classic site, you may refer to the following steps to add your task list to a new web part:
1.Click the gear icon > Edit Page;
2.Click the Insert tab > Web Part > select your task list > Add.
Regards,
Nathan
>
Edit page.