Extended ucas application

I am studying a level resits online and looks like one of my tutors won’t be able to give me a predicted grade before the deadline so I’ll only have 2/3. They’ve told me to ask the uni if they’ll consider offer an extended application or grace period. How do I go about this and is it likely to be offered?

I think they just want you to ask whether the course is likely to remain open past the initial deadline date. A lot of courses do. So it depends what the uni says and when that prediction can be provided. You'd need to call the uni as it is so close to the Jan deadline. An email won't be answered in time.
In terms of a 'grace period', that would be more a case of more a case of applying with current grades and predictions, and then contacting your choices to advise when the last prediction might be provided. Some wouldn't even need it. But others might want to wait - again, entirely down to the discretion of the uni.

Ah that makes sense thank you.

I assume this is less likely to me offered with more competitive unis, in this case is it still worth applying by the deadline with a grade missing or will that ruin my chances?

I don't think it will disadvantage you too much. Ideally your referee will comment on the missing grade and just say when it should be available if needed.
Hypothetically, yes a uni could reject you without it, but with most applications if anything is missing, they'll get in touch to request it rather than rejecting you straight away.
Personally I think it is worth the risk, so long as you are applying to a range of grade requirements. Otherwise there's not really much you can do about it point other than calling your choices as above.

Ok this seems like the better option for me. Do I need to contact the unis to tell them/ check that this is ok or can I just ask my referee to state this

You can just ask your referee to include a comment about it.
I would recommend sending an email yourself to your choices, shortly after submitting your application. Just draw their attention to your circumstances as detailed in your ref, and ask them to let you know if they need any more info.