I found the best way forward was to do the 'reputation increase' missions.
You won't make much money on them (as there is usually no payout for them) but your rep will go up faster.
Be sure you're doing them for an Empire aligned faction in whatever system you are in (ignore ones for the Independents).
They normally involve delivering non-lethal weapons, foodstuffs, or freeing slaves (NOT Imperial ones - be careful here).
When you've gained enough rep, you'll see a 'Progression Opportunity' mission appear on the board (possibly more than 1 - only take 1!) and carry it out for the next rank.
Then rinse and repeat as necessary.
Oh, and if you get a permit, accept it, but don't feel you have to go there, as the 'rep' missions will keep coming wherever you are.
If you go like stink before Powerplay you may be able to get to the rank you want!
I got this just yesterday:
Mostly from the Lao Zi, Gandui and nearby systems run.
Take Pro Cells from Dixon in Gandui to Sutcliffe in Lao Zi, then return with Gold - makes a mint, and when the 'rep' missions come up, everything you need is within a 20ly radius...
Have fun
