Admittee describes such a person.
From Webster’s:
:a person who is allowed to enter a place (such as a college or university) :a person who is admitted
But the college can’t know :a person who is allowed to enter a place (such as a college or university) :a person who is admitted. Worse, it can’t know which ones. In putting together its admittee list it took great pains to strike a balance—men and women, athletes and musicians, black and white, rich and poor. —James Fallows, The Atlantic, November 2003
The most common way I have read colleges and institutions referring such people is simply as “admitted candidates” or “admitted students”.