Hey soundlust, it's looking pretty good! The character design is pretty nice, and the color palette is working well. I did an edit for you to show you how to go a bit further in your rendering. I kept your original palette with the exception of changing your black color just a bit. Here's a few notes I wrote up while I was editing.
-Try to integrate your colors together. This is especially important in low color counts but it's true for all artwork. Colors bleed on to each other. Especially when they are bright like that green shirt. It helps to create unity in the piece when you "borrow" colors from nearby objects. You can see I added the blue shadow color to the green and add some green light reflected on some of the dark blue cloth.
-Try to light the character as a whole object and not as pieces. You did a decent job with lighting in the original but it still seems like you fell into the trap of lighting each shape separately. What I mean is that each green piece of clothing has both the bright green and the shadowed green in it. Don't be afraid to allow some pieces of green to only have the dark green. You want to light the character as a whole not it's individual parts.
- Don't outline your character in a pure black outline. When the outline is next to a brightly lit area use a darker shade of that color. Imagine a black outline being lit as well. The dark outline needs to be lit as well. Also, try and round out some of your edges on your outline, you don't want the line art to show through so much in your final colored version. I changed the color of your pure black just a bit to a slightly lighter and more brown hue color. Pure black tends to be really heavy and makes your image feel flat.
-Don't be afraid to cast areas of your character into shadow. This is a hard habit to break. Usually we want to show all the little detail we added in to our character but if you allow some of your detail to become lost in shadow it will be better in the end.
I hope this helps. Keep posting. I really like the design and color! Let me know if you have any questions.