Addressing royalty
I did research and it says use "Your Highness/ Your Majesty" for the first time then "Sir" or "Ma'am" subsequently.https://www.royal.uk/greeting-member-royal-familyBut what does it mean by subsequently? Is it per conversation or forever? For example, I met them for the first time today so I addressed them "Your Highness/Your Majesty". I will meet them again tomorrow, I can just start my second conversation with "Sir/Ma'am", right?

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yes subsequently means thereafter, for your context.
 Or for other contexts it could or would mean, the events that happened after, which is "thereafter". By definition.