How exactly does one "seal" a Gear? I know in Justice's case, she was sealed in a Dimensional Prison, but what about Gears like Hyrda? Also, "sealing" a Gear is pretty much only done if the Gear is incapable of being entirely destroyed, I'm assuming?
That is a somewhat broad if difficult question.
Gears, as you may already know, were bred as bio-weapons of war...so it goes without saying that they are extremely difficult to kill when active, much less seal away into dormancy. But of course, this also depends on class of Gear and species.
Fortunately for most of humanity, once Justice was sealed (and later killed), nearly all the existing gears awaiting her orders went into a semi-catatonic state. Gears that were mass-produced after the first model, Justice, cannot operate and function under normal circumstances without her commands (unless special circumstances change their core programming).
The gears that produced the most trouble for the Sacred Order were the T-Class and M-Class Gears. Toxic Class Gears can produce massive amounts of miasma and spores that can kill off whole ecosystems if a cure is not found and administered. Megadeth Class Gears possess size, durability, and raw physical and kinetic power capable of leveling whole cities with populations of 1,000,000 in less than an Hour.
In the case of sealing a rogue Megadeth Gear...it is almost impossible to do alone, much less with a limited group of soldiers...to say nothing of trying to kill it. If it weren't for I-No and Sol's intervention, Ky Kiske would have died from a Megadeth Gear attack in 2173, after trying to take it on alone.
In the case of the Hydra who leveled London, England: Hydra had 5 heads and a great many sword limbs that tore the city to rubble. The Sacred Order couldn't do anything against it for a day and night before their leader Kliff Undersn finally arrived. He fought the beast for seven days and nights...managing only to cut off 3 of it's 5 heads and only 4 of it's sword limbs. Though the struggle and loss was great, the Order wrapped Hydra in 13 Chains, put two large boulders on the remaining heads and sealed it...as they had many other legions of Gears to fight at that time to route their forces...and for a long time, the buried Gear lay dormant and the location became a No-Man's Land. Though despite the Hydra, humans drifted back in and built a village on top of it.
Blackard Company tried to control it with Solaria, but were unable to manage it. Eventually the International Police had to initiate "Operation Last Resort": a blacktech laser satellite that obliterated the Hydra for good (after they evacuated the villagers of course!)...but once again, the scorched earth meant no humans could ever live there again for many years to come.
As for the gear Leopaldon...his whereabouts are unknown.
And lest we forget the destructive power of Dizzy.
It's worth noting, that only the Command Type Gear Justice has had the onus of being sealed in Dimensional Prison. Most other Gears fall dormant or can be contained by simpler and cruder means, though do NOT MISUNDERSTAND...Gears are still very difficult to contain!
Related to this, though...are the Forbidden Beasts. Hi-Deigokutsuipo, the 6 Forbidden Magics not only produced 2 deadly assassins, but 4 other unknown subjects, not to mention the countless other "failures" that the Post-War Administration Bureau produced.
Most notable, however...was the project Leon Maining produced by extracting D.N.A. from Zato=ONE and Millia Rage and cloning the genetic information from their "beasts" and concentrating and injecting the fluid he produced into the soldiers of the Kingdom of Calronia. He labeled his army the "God Series". The fluid was intended to increase the soldiers' combat abilities while reducing pain and stress in the field...however this caused much more problems than he realised. Not only did it cause EXTREME STRESS on the human body...it caused the body to rupture and mutate uncontrollably.
The result was a nigh unkillable army of Gears...though not even a Gear in a traditional sense...abominations born from the exploded bodies of human soldiers! At first, Maining thought he could control the beasts and called out to them, commanding them to assassinate the leader of the Assassins' Organization.
Fortunately, at the time...three Assassins who had been at odds with one another decided to band together: Zato=ONE, the leader of the Guild, his former lover (turned traitor), Millia Rage, and his loyal servant Venom. Zato had the power to fight these "Gears" on relatively even terms, through the use of his own Dark Sentinel, the Forbidden Shadow Beast Organism, Eddie. Though he could not defeat them outright due to being outnumbered. What instead occurred...was a professionally executed plan. Venom distracted the creatures by hitting their critical points with his sniping ability "Red Hail", while Zato used the "Damned Fang" of his beast to tear open and expose their chests...while Millia Rage, despite her conflicted emotions, used "Winger" to pierce each exposed Gear Core...returning the mutations back into human corpses.
So as you can see...if you can expose a Gear's core...and have the means to destroy it...you can kill the Gear. But this varies from Gear to Gear...as some are nigh indestructible.
In fact, I'd say Sol Badguy's summoned Tribe Servant "Gigant" with all his enhancements would be nearly unstoppable...of course...Servants of a Gear are unheard of to humanity...and they aren't exactly Gears either, as that method is related to Soul Sinker.
Most Seals are done either by use of a blood pact...or forming a time-space "Ouroboros Loop" that causes a small loop in space-time...the latter requires extensive knowledge of the 12 Steps and possibly Forbidden Magic itself...beyond what humanity currently knows and utilizes. Most complex barriers are called 4ths for short because of the complicated notation.
There is a third method of forming a seal...but it's currently unstable and the method has yet to be fully researched. Transmuting an OutRage into a seal...this has only been achieved through use of Ky's sword Thunderseal...but we do not know how he did it exactly. This particular seal was meant to stop the Maiden of the Grove from eroding into sublimation, with the hope that one day she could be restored. Regardless, once a Gear has been fully sublimated...it's uncertain if they CAN be restored...or if they are gone forever.
Gear cells are links into the Backyard...Gears can still be sublimated and broken down, regardless of their dormant status. The method Valentine used to sublimate Gears goes outside the realm of the 12 Steps, so it is most likely impossible for normal humans to grasp the incantation.
Perhaps the Gear Dr. Paradigm will someday provide us with the answer!