You're not asking permission here — you're keeping the manager looped in so they know what's happening across the floor, and so they catch it if the same issue is happening at more than one table.
With one manager, there will be moments they're tied up at another table. Don't let a guest sit in silence waiting:
"I'm grabbing my manager for you right now — they're just finishing up with another table. I'll have them over here in just a moment."
Then actually go find them, and check back with the table within two minutes even if all you can say is "still tracking them down for you." A table that's been acknowledged waits much better than a table that's been ignored.
"I'm so sorry — this isn't what you ordered. Let me get the right one fired right now."
Get the correct item moving immediately. Don't wait for the wrong plate to be cleared before telling the kitchen — flag it the moment you see the mistake.
"I'm sorry it's not what you expected — would you like me to bring you something else, or adjust it?"
This is not a kitchen error, but it's still fixable by you. Offer a swap. Loop the manager in after, especially if it turns into a comp request.
"I want to give you an honest update — the kitchen's running a bit behind on your order. I'm keeping an eye on it and will let you know the moment it's close."
Don't promise a specific number of minutes unless the kitchen has actually told you one. A vague promise you can't keep is worse than an honest "I'm checking." If the table's frustration escalates, this becomes a Tier 3 — get the manager.
"That one's not running tonight — can I get you something close to it instead?"
Recommend from the standing list in the Food Guide. Keep it moving — don't explain the staffing reason to the guest.
"Let me grab my manager so we can take care of that properly for you."
Do not promise anything yourself — not a free item, not a percentage off, not a future gift card. Get the manager and let them make the call.
"I'm getting my manager right now — please stay right here."
Do not diagnose, do not guess what caused it, do not offer food or drink to "help." Get the manager immediately and let them take it from there.
End of shift: tell the manager about every Tier 2 and above issue before you clock out, even if it felt small and got resolved. With one manager covering the whole floor, this is the only way they catch a pattern — like the same dish coming back wrong twice in one night.