Hey Oliver! Have you heard of F-LEX (paralegal agency) 100% recommend them, I am with them and they really help you with long term and short term positions, whether with law firms or in house positions.
I have linked the website which will explain what they do and how it works much better than I!
https://flex.legal/
But in terms of cover letters, what I do is try and use vacation schemes and other relevant experience to highlight why I am best suited to the position. I hope this helps!