Hi Cmdr, carefully read and follow the instructions here...
Greetings Commanders, We’re pleased to announce that, starting today, we’re implementing a new and revamped application system for Player Minor Factions. In re-working the original system for applying for a player minor faction, we are now able to process player minor faction applications with...
forums.frontier.co.uk
Register your player group first, then apply for a faction. If you get it all correct you should see your faction in-game within a week or so. Note that your system description won't appear until after the next game client update. Good luck.
A few tips:
Choose your home system carefully. You don't want to get wiped out straight away by an aggressive player faction next door.
If you're in a Powerplay area, check that your government type doesn't conflict with the power's needs. It won't end well
When you write your system description, be creative, it's in the game forever. Make it memorable. There's probably way too many that read "<faction name> are a group of mercenaries feared throughout the galaxy who enjoy Bounty hunting, exploring, mining, trading and welcome new players".
They're adding them faster than ever
There's usually 5-6 more every week.