It's no different to reputation with the federation or empire (you don't gain anything tangible by getting allied to either, except a positive impact on reputation gain with minor factions and a slight variance on how the AI reacts to you in certain situations - ie how you're greeted, how often you're scanned). Whilst reputation is important to enable the faster reputation gain with affiliated minor factions and so faster unlocks for missions (and so the rank missions for feds and emps and also missions for permits), there's no direct reward for it.
It's there as a measurement of your reputation in reaction to your actions and has an impact on how the game reacts to you. It's not a grind wall to overcome. It's closer to a lore feature than anything else.
It's definitely nothing to do with ships. That's not to be confused with ranks, which Alliance never had (not certain they ever will do either, they're not a military entity, that I'm aware of).