Time spent researching the specific school is generally worthwhile. I think that you will need to look at the format of the tests carefully, so that you know what subjects are tested, and the format of the tests, as technique is quite different and a subject such as English could be tested by comprehension exercise and written exercise, or short answer questions, or multiple choice questions. Certain schools also vary the English writing exercise considerably (as it tends to be the key differentiator). So some schools adopt a "continue this story" approach, some ask for a descriptive piece only, others stories, others ask to write someone a letter etc.
I would say that concentrating on attaining as wide a vocabulary as possible, and in particular helping your niece deduce possible meanings from the text would be key. Many private schools have some form of verbal or numerical reasoning test, and a wide vocabulary is helpful.
In terms of English exams, papers usually have a comprehension paper which will test inference, and may include some grammatical or vocabulary questions. There is also a writing exercise. For the former, children are meant to study the marking scheme to deduce how much to write, and how much evidence to quote to back up their point. For the latter one is usually taught that this is an exercise to show both that you can answer the question and demonstrate what you know, so working on similes and metaphors, direct and reported speech, correct use of punctuation, and "difficult" vocabulary used correctly.
If there is going to be a verbal reasoning paper, then it is about practice, practice, practice. There are a number of good books on technique - often a child will have a gap or mental block with one or two types of question.