the Northern Ireland
The correct form is just Northern Ireland. We don't use articles when talking about places.
just got a contract
No need for the word "just". We use "just" to talk about actions that happened recently from the present moment. Since we are using past tense to tell the story of Julie's childhood, we do not have a recent even. Correct form is "got a contract".
Maybe it's the matter of nurture, maybe - of nature, but the Flints are really good at sports and have a really good chance to start another Quidditch dynasty.
The correct form is "Maybe it was a matter of nurture, maybe of nature, but the Flints were really good at sports and had a really good chance to start a new Quidditch dynasty.
We always need to keep the tenses we used before. If we are using past tenses we cannon insert a present tense or a future tense.
what surprised a bit her father.
"Which" surprised her father a bit. We cannot use "what" in that way because "what" is just a question word and not a pronoun.
Julie never was a good student
Julie was never a good student. The verb usually stays on the second position in the phrase.
Luckily to her
Luckily for her.
And despite of the fact
Despite the fact. No need to use of here as it serves no purpose.
on in her 3rd year
on is unnecessary. Probably just a typo from you
so close to be expelled
Really close to be expelled. We cannot use "so" unless we also use "that". She was so close that...
and if she wanted she would beat her up.
she could beat her up. We use would for wishes and could for possibilities.
one's self
oneself
allowed to Hogwarts
allowed at Hogwarts. We use at in this case because to is used to show direction of movement.