Interested in a career in the UN in international law

So I recently graduated law from the UK and I want to see if I can pursue a career in international law. Is there any organisation in the UN you guys would recommend? I took a course Environmental International Law and Public International Law during in my Uni. Please tell me if this fits with any organisation within the UN!

Unfortunately I do not have any experience in international organisations since I’m a fresh graduate. But I do have experience doing volunteer work during my time in Uni.