The vote, by the UK electorate to leave the EU, was just a vote. By itself, it does not alter the legal relationships of the UK, Europe and the rest of the world. First of all, the formal process of termination must commence pursuant to Article 50 of the Treaty on European Union (TEU) with a termination notice from the UK government to be given in accordance with the constitutional requirements prevailing in the UK, which will start a two-year period (Sunset Period) of negotiation on the details of the withdrawal (Withdrawal Agreement).
At this point, there is no certainty as to when the UK government will issue the notice of termination of its EU membership. Therefore, there is no certainty as to when the Sunset Period will commence, meaning that the actual date of Brexit remains uncertain.
However, to read more about how Brexit may affect dispute resolution practices, generally.