
Can I write without leaving my job?
I want to write dramas and plays. But I'm an analyst who works at the bank. I've written stories before, and I hadn't really bothered to see how well I had done. But in hindsight, I've realised that I write really good stories. Is there a way I can write something and just give the script to someone who works in theatre/media? Is that a smart way to do my hobby, or is it a useless idea?

Why do you care about what your workplace thinks? It's not a conflict in any way, and it's anyways stupid to tell them about it. Just earn your money, it is not illegal.

I don't care about my workplace. I just don't know how I can write with a purpose. Like okay I write something, then what? Whom should I give it to?

Best way is to find work under a senior writer who is currently working on movies and TV shows. Hard to reach them though, they are usually spammed by many writers. If you have contacts it'll help.
You can also change the format, make your own insta page with comics/AI animation/voiceover formats of your stories. Good way to gain attention if your stuff is really good and well made.