For upper juniors, QCA Unit of Study 15 is "The Mountain Environment". The exploration of Everest could be the core of this unit and would allow both its key questions (eg ''What is this place like?") and its optional questions (eg "What would I need to do to plan a camping holiday in this area?" to be answered.
At key stage 3, and through to GCSE, there is a range of links. An interesting one to investigate would be the impacts of tourism, both positive and negative. Unit 19 of QCA's scheme of work (Tourism - good or bad?), which has a particular emphasis on sustainable development, would provide a useful framework.
The cultural dimension of the Everest story is perhaps most suitable for post-16 geographers. Why do we know the peak as Everest, and not Chomolungma (Tibet) - or should that be Sagarmatha (Nepal)? Why was a New Zealander first to the summit? Why did Edmund Hillary receive a knighthood but Tenzing Norgay only a British Empire Medal?