It's not really a court for Europe, it's a court for the EU, two very different things. And outside the EU the UK will not be allowed a representative on the court.

The EU is how most of Europe organises itself, as the UK is finding out, it's very difficult to be a developed country in Europe while insisting that "The EU is not europe".

It's a slogan I saw many times on brexiters timelines though, I find it to be as useful as saying "The UK is not britain" or "Love British isles, hate the United kingdom".

And outside the EU the UK will not be allowed a representative on the court.

Not every EU country has a "representative", by which I think you mean either judge or advocate general. That doesn't matter anyway, the rules are that the ECJ's judges be an EU citizen, each country doesn't get to send their own representative.