Can you cast an instant during the cleanup step if a hand-size discard trigger goes on the stack?

Normally, no player receives priority during the cleanup step, and no spells or abilities can be cast or activated. The cleanup step simply has the active player discard down to maximum hand size, then damage is removed and 'until end of turn' effects end (CR 514.1).

However, CR 514.3 creates a critical exception: if one or more triggered abilities trigger during the cleanup step — including a discard-triggered ability — those triggers are placed on the stack, and then players do receive priority in normal turn order. This means you can cast instants, activate abilities, or do anything else you could normally do during a priority window.

Once that priority window resolves completely and the stack is empty again, another cleanup step begins. If nothing new triggers during that new cleanup step, it proceeds normally and the turn ends (CR 514.3).

Concrete example: Your opponent controls Waste Not, which triggers whenever a player discards a card. During cleanup, you discard two cards to reach maximum hand size. Both Waste Not triggers go on the stack, players receive priority, and you may cast a Lightning Bolt before those triggers resolve.

The key rule to remember is CR 514.3: a triggered ability firing during cleanup is the 'unlock' that grants everyone priority for that window.