Why not هُناك ألجامِعة ?
Because in this case you have to start with the subject.
You can say هناك جامعة (so without the definite article), but then it means "there is a university".
By the way, it's الجامعة (no hamza on the alif).
I don't know the difference between الجامعة with and without the hamza
Just remember that the definite article ال is never written with a hamza.