How do I add or remove application forms from my page?

Overview

There is no separate list of forms on your organization page. What a form shows there is decided by one setting: its privacy.

Public. The form appears on your organization page.
Private. The form does not appear there, and is reachable only by its direct link.

So adding and removing a form from your page is the same action as changing its privacy.

Go to your Forms page.
Click the 3-dot menu to the right of the form.
Click Set to Public to put it on your page, or Set to Private to take it off.

The change takes effect immediately.

Behind the Get involved button on your organization page. Someone who presses it is offered the forms you have made public.

Yes, and this is the part worth knowing. Several forms can be public at the same time, and the visitor picks from them.

That lets you split your intake by who is arriving rather than funnelling everyone through one form:

Give them names that make the choice obvious from the outside, because the form title is all the visitor has to go on.

No. Private means it is not listed on your page, not that it stops working. Anyone holding the direct link can still open and submit it.

If you want a form to stop accepting responses altogether, close it to new submissions rather than setting it to private.

Privacy is the setting that adds or removes a form from your organization page.
Forms, then the 3-dot menu, then Set to Public or Set to Private.
Public forms sit behind the Get involved button.
Several forms can be public at once, so you can split intake by audience, event or language.
Private only hides it from the page. The direct link still works.