Hello! L'université means literally "the university", as a noun. For example, the university of Paris - L'université de Paris. Universitaire is an adjective, meaning something related to the university, for example: the university library is called "la bibliothèque universitaire". I hope this helps!

The previous answer is perfect, so just in more simple 'université' it's the place/ the institution; and 'universitaire' is used for everything related to the University.