Last week, my gel pen leaked in my shirt's pocket, colouring it black.
Is there any way to remove these stains?
Use some kind of sanitizer (yea, the one you use to clean you hands!) Just apply some in the ink stain and wash, and apply again and wash, Boom! Stain's gone!
Alternative; Dip the stained portion in milk overnight, wash in the Morning,it'll surely go!
Ethanol, as in hand sanitizer, as @QuestionEverything sugeests, is an effective first step. However, to get "black" ink, a number of different dyes are used, so other solvents may be needed in order to remove residual colors. In order, I'd try:
Finally, if it's a white shirt and can withstand it, a bit of bleach in a lot of water.
I used Wd-40 on my carpet and left it for a couple of minutes and then I used warm water to rinse it. It worked very well. Try using this on your pocket.