There are a number of differences between a good university History essay and a good A Level History essay. While both look for a clear answer to the question, a clear writing style and good knowledge of the subject matter at hand, university History essays require freshers to do a few things slightly differently, which may come as a surprise after having trained to produce essays in a very particular way for A Level exam papers.
Primarily, university History essays look for one, central clear thesis. At A Level, we are encouraged to maintain a balanced argument throughout. At university, everything in the essay must relate to our central thesis- counter arguments should be recognised, but don't be afraid to critique them, in support of your own argument. At university, your History essay should also interact with what other scholars in the field are saying. While a good A Level history essay requires good subject knowledge and contextual examples, at university you should show that you have read relevant literature to the question you are answering, being clear about what this adds to your answer. For example: X says that the Weimar Republic struggled with Y because of Z. This has considerable merit given that... Finally, university History essays require you to have a comprehensive knowledge of referencing to do well. Each university has their own preferred style, however I will show you a basic footnote: endnote referencing technique. Make sure you keep your referencing style consistent throughout!