What is the term for a postsecondary school that has set of requirements admission?

There isn't one single term to describe all postsecondary schools with admission requirements, as *all* postsecondary schools have some form of admission requirements. However, depending on the *type* of requirements, different terms might apply:

* Selective college/university: This term is generally used for institutions that have highly competitive admission processes, with low acceptance rates and rigorous academic standards.

* Competitive college/university: Similar to "selective," but perhaps slightly less stringent.

* Institution with entrance examinations: This describes schools requiring standardized tests like the SAT or ACT as part of their application.

* Institution with application requirements: This is a very broad term, encompassing all postsecondary schools, since all require *some* form of application and associated requirements.

Therefore, the best term depends on the *specificity* of the requirements you want to emphasize. If you're talking about schools with high standards and low acceptance rates, "selective college/university" is appropriate. If you need a more general term, "postsecondary institution" or even just "college/university" will suffice, keeping in mind that all of these have admission requirements.