I can tell that you're already a leader. Just by knowing yourself well enough to know that you're an introvert, knowing that you want to become a leader/manager, and asking others for their input on how to develop your skills to get there - it's clear that you have emotional intelligence, which, according to the Harvard Business Review is a key leadership skill.
Leaders come in many forms - and you'd be surprised at how many of the world's greatest leaders and most successful people consider themselves introverts. Bill Gates, Mark Zuckerberg and Elon Musk have all identified themselves as introverts. Fortunately, leadership isn't about who speaks the loudest, or who commands the most attention in the room (quite the contrary). What's more important is how you treat others. If you approach interactions with humility, and with the intention of making others feel good about themselves, you'll find that people will gravitate toward you and your ideas, allowing you to inspire, motivate, and develop others.
It also helps to "just do it" when it comes to overcoming shyness. I used to be incredibly shy when I first started this job and after regularly having to take the lead on initiatives and work with others as part of my job, it got easier and easier.
Best of luck!
Karen recommends the following next steps:
- Research "introverted leaders" online
- Research "emotional intelligence" online