Can you cast an instant during the cleanup step?

Under normal circumstances, no player receives priority during the cleanup step, which means no one can cast spells or activate abilities. The cleanup step exists solely to discard down to maximum hand size, remove damage from permanents, and end 'until end of turn' effects (CR 514.1, 514.2).

However, there is a critical exception: if any triggered ability triggers during the cleanup step — or if a state-based action needs to be performed — a new cleanup step is generated. In that new cleanup step, players do receive priority and may cast instants or activate abilities as normal before the extra cleanup step resolves (CR 514.3).

Common triggers that can cause this include abilities like 'at the beginning of the next cleanup step' or effects that trigger whenever damage is removed from a creature. Once those triggers are put on the stack, players regain priority and the game proceeds with a full round of priority passes before another cleanup step is created.

Concrete example: Your opponent controls a creature with the ability 'Whenever a player discards a card, this creature gets +1/+1 until end of turn.' During your cleanup step, you discard a card to hand size. That ability triggers, so a new cleanup step begins where both players receive priority — you could now cast an instant like Giant Growth before that new cleanup step ends.

So the short rule is: instants cannot be cast in a normal cleanup step, but any trigger or state-based action during cleanup spawns an additional cleanup step where priority is granted and instants are fair game (CR 514.3).