At the moment we know that Shamrock is the commander of the HKs. However Garling was introduced as Supreme Commander of the HKs, before he became Gorosei.
This suggests there is at least one HK higher in rank than Shamrock.
It being Gunko’s father would make sense. Rather than introducing him in God Valley, Oda gave this guy his own introduction. He’s the villain of a flashback, and likely responsible for most of the terrible stuff that happened to Gunko and Esperia.
I think like Gunko, he has some form of immortality and is basically a pseudo-Gorosei. We’ll see him next arc, possibly as burn scar man. Eventually once he gets defeated, Shamrock will replace him as supreme commander in the final war.