Am I required to clear the use of class, race, or sub-race found in sources outside of the PHB with my DM?
The short answer is yes, although required might be too strong a word.
From my experience anything outside of the Player's Handbook should be cleared by your DM. Now the DM may also give you a list of pre-approved books that you may choose character options from, but this should be discussed also.
Further, from my personal experience, it is a good idea to even discuss the class, race, and subclasses from the PHB with the DM. When I DM, I appreciate being asked questions and discussing what my players are choosing, and I also enjoy giving them advice when they wish it.
For most D&D groups it's praxis to clear any characters you make with the DM.
You're going to play the game together so it's good to get on the same page about things. D&D 5e can be played and ran in so many different ways—it's kind of the "all things to all people" edition—so it's good to talk to each other about the game world, the way the game is set up, the characters you intend to play and so on, especially if you're just starting out together.