Sie gibt daraufhin ihre Ausbildung wieder auf.
gibt auf means stopped education?
We haven't been given any context, but it's probably like the "again" in "And then she gave the book back again".
As in, she started her education, and then she stopped again.
Of course, it's possible that it's also used in the literal meaning, where she had dropped her education in the past already, and this time she's doing it again.