If you mean the "First Oath">"Stargazer" rank thing, by spending Coins.
But since you have a limit to the number of leaders you can get depending on rank, this means that you can only spend so many coins on recruiting level 1s, so unless you fire them to re-hire them, you need your leaders to get some levels so you can spend coins on upgrading their skills.

Thanks for the answer.

Since there is an another reputation? system in the mod, i advise against firing them after you recruit them, because doing so will lower that ones standing. The general idea (i guess) was to recruit a leader and "raise" them, since getting a talent needs Star Coin aswell, and certain leaders can upgrade their unique skills aswell which costs Coins too. But these should be in the ingame tutorial section too. If not i will update/change the relevant section to reflect this later on.

You rank up by spending Star Coins on hiring/upgrading leaders.
Level 2 takes 50 coins, level 3 takes 100 coins, level 4 takes 200 coins, level 5 takes 500 coins, and the max level takes 1024 coins spent.