The activity hasn't started yet

We recommend that you make a special activity for un-registered customers in order to be able to follow up with marketing and the like and simply switch the registration to this activity. Or you can just delete the registration (note that this also deletes the invoice).

The activity has already started

Set the 'End reg time' according to your terms (today, the end of the month or...) and adjust the price accordingly.
This will also ensure that this registration doesn't roll-over to the next term in any of the automation.