We just got off the Royal Princess yesterday, after an amazing Alaskan cruise, and there was no regular afternoon tea service in the dining room, let alone any Royal Afternoon Tea being offered.
We were very surprised because we thought tea service was a daily standard on Princess.
There were a few scones, cream, and jam available in the Horizon Bakery but not really the same experience.
On a bright note, afternoon tea is available to Elite CC on request and we were able to enjoy that in our cabin.