Can you move an equipment to a different creature at instant speed during combat?

Equip is an activated ability with the cost usually written as "Equip [cost]: Attach this permanent to target creature you control. Activate only as a sorcery." That last clause — "Activate only as a sorcery" — means you can only activate the equip ability when you could cast a sorcery: during your own main phase, when the stack is empty, and when you have priority (CR 307.1, 602.5a). So by default, you cannot activate the standard equip ability during combat.

However, some Equipment cards have alternative or additional equip abilities that do not carry the "activate only as a sorcery" restriction. A classic example is cards with Equip abilities granted by effects like Leonin Shikari (which lets you activate equip abilities at instant speed) or Equipment that explicitly say they can be equipped at instant speed. In those cases, you can absolutely move the Equipment mid-combat.

Additionally, other effects — such as spells or abilities that say "attach target Equipment to target creature" — can move Equipment at instant speed even without a special equip ability, since those are separate spells or triggered/activated abilities, not the equip keyword itself.

Concrete example: You have a Sword of Fire and Ice attached to Grizzly Bears, and both are in combat. You want to move the Sword to your Llanowar Elves. You cannot activate the normal equip ability right now because it's combat, not your main phase. But if you control Leonin Shikari, you gain permission to activate equip abilities any time you could cast an instant — so you can pay the equip cost during the declare blockers step and move the Sword to Llanowar Elves.

In summary: standard equip abilities are sorcery-speed only (CR 702.6a), so they cannot normally be used during combat. You need a special rule, card, or effect that explicitly grants instant-speed activation to move Equipment mid-combat.