These types of sentences always feel a bit like a sucker punch. I missed where it said anywhere how the words "cuireann" and "áirithe" used together could/would mean "reserve" (at least that's what I'm left to assume) and this is the first time I've even seen "áirithe" used.
It came up in an earlier question in the lesson in my case so it must be the luck of the draw.
Literally it means She puts the restaurant in certainty.
Ó Dónaill gives the following seanfhocal (proverb) for A bird in the hand is worth two in the bush:
Is fearr áirithe na srathrach ná iasacht na diallaite.
Literally it means The surety of the straddle is better than the loan of the saddle.
A straddle in this context is a piece of harness that goes on the back of a horse when it is pulling a cart.
There’s more than a few instances of this sort of thing, so you might as well get used to it.
Irish really seems to like this kind of complex, idiomatic construction. It's delightful at times, but sometimes it can be a bit wearying.
With me is more the way the words "in áirithe" are run together by the speaker. It comes out more like "i náire ingear" which makes no sense at all. She is the sharp high restaurant?
After another year has passed I can hear "in áirithe". Newer learners shouldn't give up. Your ears will attune, given time!
Does this mean she makes a reservation at the restaurant, like a dinner reservation? or does it mean she reserves the whole restaurant?
My guess is she makes a reservation. But I've been wrong before. Give me another year. ;^)
It means "She reserves the restaurant". Whether you interpret that as she is reserving the whole restaurant, or she has made a reservation will depend on context. If I was making arrangement to meet someone for dinner and she offered to reserve the restaurant, I wouldn't expect to have the whole place to ourselves.
There is no additional meaning in the Irish sentence that isn't there in the English sentence.