There are quite many clubs you can join.
KCFA and Karachi Flames at NCC as mentioned above. KCFA's timings are mon,wed,fri 5ish onwards till maghrib. if you're good enough they might take you in their 1st teams. No idea about Flames. but they are very good. especially their head coach maam bhai!
Then there's Karachi United in Defence. Its a proper football academy. but dont expect any first team experience. Their 1st team consists of only the best of the best, highly experienced players. visit their official Facebook page for more info.
You can even join Fanats FC. Again in Defence.
There's one in Malir Cantt. The name has just slipped out of my mind. They are one of the best local teams of Karachi.
The last one i know about is in Khokrapaar, Malir. But it might be dangerous for you to go there these days. there's a football ground, go there and ask anyone about the local team. they would tell you.