Can you cast a spell with suspend after its last time counter is removed if you don't have priority?

When a card with suspend is in exile and its last time counter is removed at the beginning of your upkeep, a triggered ability triggers that says: "cast this card without paying its mana cost." This trigger goes on the stack like any other triggered ability (CR 702.62d). You do not manually choose to cast it — it happens automatically as part of resolving that trigger.

The key point about priority: triggered abilities are placed on the stack the next time a player would receive priority (CR 603.3). Once the trigger is on the stack, players receive priority in normal turn order. When the trigger resolves, you cast the spell — this happens as part of the trigger's resolution, not as a separate action requiring you to hold priority (CR 702.62d). So you don't 'cast' it by spending your priority; the trigger does it for you upon resolution.

However, opponents do receive priority after the trigger is placed on the stack and before it resolves, meaning they can respond to the trigger (e.g., exile the suspended card in response). If the card is no longer in exile when the trigger resolves, the cast simply cannot happen.

Concrete example: You have Ancestral Vision in exile with one time counter. At the start of your upkeep, the counter is removed and the suspend trigger goes on the stack. Your opponent may cast Surgical Extraction in response. If they don't, the trigger resolves and Ancestral Vision is cast automatically — you never needed to spend your own priority action to cast it.

Relevant rules: CR 702.62d governs the triggered ability created when the last counter is removed; CR 603.3 covers when triggers are placed on the stack; CR 117 covers the priority system.