What are the career opportunities that I get in Singapore or any other country after graduating from NUS with an LL.M in International Arbitration & Dispute Resolution?

Unlike something like an MBA for example, an LLM isn't really a degree that easily facilitates country / region switching. Most LLM graduates tend to go back to their home countries after the degree. A main reason for this is that it can be extremely difficult to be able to practice law in a country where you did not do your undergrad in law.

However, legal jobs where you're not actually practicing law exactly - such as working in an NGO or a consulting firm - may be possible.

You'll need to talk to the school directly and ask them about what level of career support they provide, and, importantly, real examples of students who've landed jobs in Singapore after their LLM.