The feeling of being an old soul is exactly why I was so drawn to trying to find out more about my past lives 
Of course! You need a candle and a mirror. First I like to cast a circle - I always do when I do any spellwork - although I’m sure if it doesn’t fit your practice it’s also fine without.
Then, light the candle and place it next to the mirror, so that it illuminates your face. I prefer the room to be relatively dark otherwise. Then, say the following (I actually found this little chant on Pinterest, though I believe I adapted it a little bit!):
Remove the chains of time and space
And make my spirit soar
Let these mortal arms embrace
The life that came before
Oracle of lunar light, bless me with the second sight.
Say this as often as it feels right while looking into the mirror.
Usually, my face in the mirror gets a bit blurry after a while, like other faces are overlapping it. When that happens, I like to close my eyes to open myself for any images or visions that might come.
I have done this spell about 6 or 7 times thus far, and it really works well for me. Most of the time I catch little snippets of my past lives; it’s a bit like watching a scene from a movie for a couple of seconds, before moving to the next scene from another movie and so on. Twice, however, I experienced longer memories (if you wanna call it that) which lasted for maybe a couple minutes. In any case I like to use my pendulum afterwards, to verify what I saw - making sure I didn’t misinterpret anything - before noting everything down 
If any of you try this out, please share your results 
I would love to hear about other peoples experiences with this as well.