Ah okay, so yes that is powerplay and a different thing.I've not explained myself right. It's not just the getting to allied status by completing missions.
It's on the 'Galactic powers' window, where I can choose to 'pledge allegiance' to one of 11 powers.
I've also never worked out how to do anything about combat bonds.
There is only one real reason to pledge with someone and it's their unique unlocks. Lots of them are very good (prismatic shields, cytoscramblers etc).
It takes a month of being pledged before you become eligible for those rewards, so it's worth pledging now, waiting 4 weeks and then carting 750 of the special cargo (you're gonna need about 7m credits) for preparing a system for takeover. Then the following Thursday you'll be rank 3 and can buy the special unlocked module. You'll need a lot of credits because you are never going to buy these things again without having to do this whole cycle, so buy as many as you think you could possibly need. For prismatics you're going to want about 350m credits, for others you will only need a fraction of that.
As soon as you have that done, you abandon the power and start on the next one. Obviously it takes a year to do 12 powers so get started now.