appropriate Word for transfering student from one university to another university
You could simply use the term "transfer student" that you've already used in the question tags.

Collin's Dictionary:


  a student who moves from one institution or course to another at the same level (e.g. undergraduate)


A student can both be said to apply to the new university as a transfer student, and be described as a transfer student at the start of their study at the new university (example).