Just like in real MMA, Submissions in EA Sports UFC 3 can be chained into more advanced submissions while in progress. Chaining Submissions in EA Sports UFC 3 is an advanced move, so you should be familiar with performing a submission before attempting to learn how to chain into more complex moves.
For example, an Armbar can be transitioned into an Arm Triangle and the game will tell you when a Submission Chain is available. Not all submissions can be chained, but when they are available a bright green prompt will light up in the Submission mini-game, prompting you to chain to the new submission. The green prompt will look like the normal submission advancement prompt, but it will be green.
If you manage to time it right, Flicking the Left Thumbstick when the green submission chain prompt is active will chain into the new submission. Alternatively, if you are on defense when an attacker is trying to chain into a submission and you Flick the Left Thumbstick first you will cancel the submission chain attempt.
After chaining to a new submission, you must continue to progress through the Submission process to eventually get a tap out from your opponent.