Hi @balzamico , just noticed your question.
DS sat the HAT two years ago and is now inks second year of history at Oxford. He went to a state comprehensive with a good history department, but even then he really needed to practice for the HAT.
I’m sure your DD has seen the sample papers on the history faculty website - it is so very important that she works with them before the exam. Each previous question comes with marking notes, so if she is finding it hard to get into, she could choose one to just make an un-timed, not formally answered first stab at, then maybe talk through the marking scheme with someone. Even just explaining her answer and how she thinks it would be marked to a parent who has no knowledge of the question would be very useful to her. she could then work up to doing full, timed practice papers (there are quite a few of them, and she should note that, in the oldest ones, only the last, long question, is relevant for practice).
DS ended up doing all of the previous papers and he was immensely glad that he did, partly because he felt well prepared for HAT and also because it got him working in a way which he has had to regularly while at Oxford.
Hope that helps, and very good luck to your DD.