Is there a way to add an event on a hebrew date, so that it repeats next year?

Yes, I know about that. But that creates a static calendar. 
If a new date comes up, I can't add it to it - I need to then create a new calendar.

Is there a way to have a live calendar that I can choose it and add to it whenever?

Our yahrzeit and anniversary calendar is not a static calendar. If you create a personal anniversary calendar and then subscribe using our recommended subscription instructions in Google calendar, Outlook, or Apple calendar, you can add new events at a later date. It will take about 24 hours for those new events to show up.

please read the following article for more detail details:

https://www.hebcal.com/home/632/how-to-make-changes-to-a-yahrzeit-anniversary-calendar