I wouldn't do anything "new" in preparation of the new subjects they're going to start learning.
BUT, having been through the transition with my son, there are a couple of things you could usefully do over Summer. I'd concentrate on basic numeracy/literary skills - yes, I know she must be good to have got a high enough score in the 11+ to get a place, but there's always more to learn and the grammar school won't actually do too much at the basic levels in these core skills (they'll assume their pupils are already there).
Re literary skills, just lots of reading, to improve vocab, grammar, spelling, and get more ideas of different types of stories, subjects, etc. Aim to go onto older/more complicated books rather than staying at her current reading level - an ideal time for you to read with her to help her get onto more adult books.
Re numeracy, I'd strongly suggest you teaching her how to do long multiplication and long division and also adds/subtracts, with the old fashioned "bunk bed" approach of columns of units, tens, etc. Many primary schools don't do this well at all and concentrate on relatively small numbers which are more suited to the modern techniques taught, but aren't really good enough when you're onto huge numbers. The grammar expects their intake to know how to work with big numbers from day 1 and won't have the time/inclination to go back to basics for those who are struggling.
Our son, who got SATS level 6 in Maths really struggled at grammar when working with huge numbers without a calculator. School weren't any help so we had to work out for ourselves what was wrong, and when we sat with him and watched him step by step through the calculations, we saw what crazy convoluted methods he was trying to use (I think they call it the grid system), which had untold possibilities for making errors. We put a few evenings aside and taught him the old fashioned long methods and he took to it like a duck to water, then we printed off some worksheets from the corbettmaths website, and he was suddenly able to do it quickly and accurately. At the next parents' evening, we mentioned it to his teacher who glibly said, "oh yes, a lot of primary schools don't teach it very well" and went on to say that there isn't really the time or inclination to do it at the grammar because most pupils can already do it!