As someone very closely involved in trying to get a new club sport started, it is near impossible, but they'll keep giving you hope.
Basically you'll put in an application each year demonstrating why your Extracurricular Activity deserves upgrade to a club sport, including things like facilities, coach, who you'll compete against, etc. You'll do this once a year, probably get some false hope, and then get rejected.
Then again, if you're promoting a new women's sport, you've got some politics on your side and might be able to make it happen.
Now if you can't get an officially approved club sport, you can still compete, you'll just basically be doing it on your own time. You'll probably be able to get it approved as an ECA, but unless something's changed, that means tournaments, etc. are on your own liberty time. This means that anytime you want to bring a plebe along for a full weekend or even just a Sunday, you will be putting up a special request chit (and there's a pretty good chance it will not get approved). You'll probably be able to get a few Movement Orders to cover tournaments, but chances are you'll probably be using your own weekends for most tournaments (we were basically only able to get a MO twice my entire firstie year, and otherwise used our own weekends).
If I sound bitter about a lot of this, it is because I was very bitter about it. If you are not already a club sport or one that the Academy thinks can get it some visibility, you will essentialy be out of luck, and be using your own time and resources to make things happen, and will be heavily limited. I don't mean to crush any hopes of doing things on your own, because it can be done, but expect quite a bit of difficulty in making it happen.