There are four stacked keys on the right side of your clarinet. Some call them "trill keys" or "jump keys". I'm only going to write about the top two, closest to the mouthpiece - the most ignored keys on the clarinet.
The top key can be used to play tremolos from open G to the throat Bb, so you don't have to suffer trying to go back and forth from open G to the Bb with the thumb and A key. This doesn't come up often and the sound quality isn't great even though the tuning is usually good, but when you need it, it's a big help.
The next key down I'll call the "Bb" key, which is one of the most important keys on the clarinet, and maybe the most ignored.
You're used to using the register key plus the A key to play the throat Bb, but that note is the nastiest sounding note (stuffy and usually out of tune) on almost all clarinets. Yes, you can use "resonant fingerings" (which I'll write about soon), but these are rarely satisfactory and can be very clumsy.
When you can, why not use the Bb side key with the A key instead of using the register key and A key for the throat Bb? Why, O why?
That fingering produces a clear, resonant, and in-tune throat Bb, not the stuffy out-of-tune sound of the "normal" Bb fingering! For longer notes when you can use it, use it! it's fantastic!
Also, you may have learned to play the high high C to D trill or tremolo using the throat Ab key. Unless you need to get your right hand fingers down in a hurry, use the side Bb key with the usual fingering for high C instead. Using the side Ab to reach the D from high C is ugly in slower tremolos, and not the best for trills because the Ab key D is disgracefully out of tune and fuzzy-sounding.
Over and out.