The main game-mechanical reason why spellcasting foci (or component pouches, their alternative) exist is that they offer a way to disarm a spellcaster by taking them away. Disarming the PCs can be used by the DM as a tool to get the party into a situation they can't solve through combat. This opens up opportunities to apply non-combat skills and roleplaying.
Many of the more munchkinesque attempts to loosely interpret what a focus can and can't be try to somehow circumvent such situations. But a ring can still be taken away just like most foci. When the ring is a very plain one, there is a good chance that one might miss it when frisking your character. But you could compensate for that by making the ring way more flashy, maybe visibly glowing and pulsating with magic power so even the dumbest NPC recognizes it as important.
But I am not your DM. Ask your DM if they allow it or not.
Probably not
The Warlock class feature, "Pact of the Blade" gives you two options to make a pact weapon:
Option 1: Creating a pact weapon
If you create a pact weapon, you can choose it's form, but are limited to melee weapons listed on the "Weapons" table in the player's handbook:
Rules answers, April 2016:
The warlock’s Pact of the Blade feature (PH, 107–8) lets you create a melee weapon out of nothing. Whenever you do so, you determine the weapon’s form, choosing from the melee weapon options in the Weapons table in the Player’s Handbook (p. 149).
So, you could select quarterstaff. But just because an arcane or druidic focus staff can act as a quarterstaff, that doesn't necessarily mean that a quarterstaff can act as a focus staff. Neither the arcane staff nor druidic staff are ordinary quarterstaffs.
Arcane staff, PHB p. 151:
a specially constructed staff ... designed to channel the power of arcane spells.
Druidic staff, PHB p. 151:
... a staff drawn whole out of a living tree ...
A created pact weapon certainly isn't drawn whole out of a living tree, and nothing in the rules indicates that it is designed to channel the power of arcane spells.
Option 2: Transforming a Magic Weapon
While, I am not aware of any magic weapon that explicitly acts as a arcane or druidic focus, Jeremy Crawford has given his opinion on twitter, that any magic wand can be used as an arcane focus. So your DM may take that into consideration, and also agree that any magic staff can also act as an arcane or druidic focus.
Also, there is nothing preventing your DM from putting such an item in your game, and per the rules you would be able to make it your pact weapon. As far as I can tell, this is your only option.
Best Answer
A magic item might be required for this
An arcane focus is usually a dedicated item.
It is not intended for it to pull double duty (as armor or weapon). This setup would also allow for you to hold something in your hand without dropping the focus. So due to this, and possibly depending on what you want to use the gauntlet for, it could be reasonable for your DM to disallow this merger.
But there is a magic item that will help you if you intend the gauntlet to be a weapon, the Ruby of the War Mage (XGtE 138). It is exactly as you describe, a crystal you set into a weapon to make it function as an arcane focus. The downside is that it requires attunement.