Making your way into this so called small club of few players. Even if it might be true, I am of the idea that the more the merrier, the more people is acquainted to arbitration, especially lawyers and practitioners, more arbitral clauses, for helping in the faster resolution of disputes, at the international and at the national level.
How to make way in this world remains a great question, either for someone just starting in the legal field, or someone that wants to change paths within law.
The starting point might be to choose while studying your LL.B. a course that includes the subject of Alternative Dispute Resolution or ADRs, as it is commonly known these set of tools for dispute resolution or to choose a course exclusively directed at Commercial Arbitration, and in conjunction joining a Moot Competition team.
However, if there is no type of courses in your LL.B. at your university, you still can find courses offered in the summer by different universities or as MOOC Courses.
In my case I was fortunate enough to have both, the possibility to have a course on ADRs and the other to be part of a Moot team.
Given that today traveling is quite restricted, you can find different online offers, one of these offers is provided by the University of Leiden, and the Course International Law in Action: the Arbitration of International Disputes, this course gives you a broad perspective of what is international law and what can be understood of international disputes, but the focus is more on the public international law side, instead of private international law, however, it is highly recommended and bang for the buck.
But, if you want to get more serious in your path towards arbitration, you can be part of the summer programs a la distance given by the different Universities and Arbitration Centers, a good example of these are the well known courses developed by the Center of International Commercial Arbitration by the American University Washington College of Law, despite the price tag per program it is worth every penny, due to the great professors involved in such a program.
So, even if you are part of a Moot team or your university offers a course within your LL.B. it does not hurt to deepen your understanding of arbitration and international disputes having exclusive courses on the matter, the above are just examples of many more.
There you go, I hope this can help in your path for breaking into arbitration!