Hi, I'm new to this site, so I don't really know how to do this.
But.. I'm looking for a protagonist, preferably male, who starts off as "low ranked" but slowly climbs the ladder to become a leader or someone with power.
An example is like the manga: Kingdom by HARA Yasuhisa

Well, here's my two cents. 1/2 Prince is one while the lead is female, her ingame character is a male.
There's also Kurogane (IKEZAWA Haruto), a real cool one.
Additionally, you can also try Sun-ken Rock.
I'll throw more in as I think of em.

One Piece

Historie-Definitely

The breaker and its sequel-though its power with mafia style houses of martial arts. Still a similar sort of thing though.

Jyu oh sei though its not being scanslated so you'd need to buy the tokyopop books or watch the anime...

Onepunch-man fits but its super hero ranking instead...and he's similar to shin in that he was powerful originally, just mainly gains recognition...

Ares maybe but its not completely like that, they more get special missions and the such but yeah...still has that feel to it...

One piece technically though its more his bounty, rather than rank, which rises. Seconded.

Magi

Gantz-though more the becoming leader part than ranks and the such.

Thanks
I'll definitely check out Sun-ken Rock, Historie, and Gantz.
(Since I've already read/ am reading the others.)

Shana oh Yoshitsune
Hunter x Hunter
YuYu Hakusho
Recca no Honoo
Shaman King
Psyren

If you don't mind something that's unrelated to battles or fighting, then this may also fit your requirement
Wild Life


What I think may fit your requirement:
Kateikyoushi Hitman Reborn!: I think this counts. Although the MC seems as weak as ever outside of battles.

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