How to Unlock New Moves in Career Mode
Go to the Training Camp screen, which can be accessed by hitting RB/R1 at the home hub in career mode. Scroll down and select Invite a Fighter, which will allow you to select a sparring partner. You will unlock a few sparring partners at the start, but most will require you to fulfill some kind of objective. You will have different goals throughout your career, such as becoming a ranked fighter.
After selecting a move, you will then moving to the training session. In order to acquire the move, you will have to hit your partner with the move multiple times, until you hit a specific score (the score will be indicated at the bottom of the screen). Once you reach the score, you can then equip the move and use it during fights.