In the phrase "My mom, the drinker of tea" what literary term is being used. I forget the name of it

"Literary" means written works. "Term" means a word or phrase. What you are asking about is a figure of speech or rhetorical device.

There are over a thousand cataloged figures of speech, and your example is a rather subtle one, so you are unlikely to find anyone who can name it from memory. For one thing, most of the catalogs were written over two thousand years ago. The field is not well studied these days. Here is a book that lists about 900 figures found in the bible. openlibrary.org/search?q=e.+w.+bullinger+figures+of+speech

You can get a printed copy at any book store.

More figures: mentalfloss.com/article/60234/21-rhetorical-devices-explained