I assume you mean "modern people who are historians" rather than the other meaning, "historians of a modern period" (I doubt ancient Latin and Greek are very useful to historians of the modern world!)

As always with questions about grad school, we can give lots of different anecdotes about own experiences, but the only way to know for sure what you need and what would be useful would be to contact the school you want to apply to. They're all different and each school knows their own requirements best.

I got my PhD in medieval history (actually "medieval studies") and Latin is extremely important. My school had really famously difficult language requirements. Everyone had to pass exams in modern French and German (the main languages of medieval history scholarship, aside from English). We also had to pass two levels of medieval Latin exams. Studying classical Latin before grad school really helped, I think most people had done that. But not everyone had, so there were intensive crash courses in classical Latin for beginners.

Studying medieval Latin mostly just involved reading, reading, reading...just endlessly reading a ton of medieval texts. Classical and medieval Latin are basically the same, but there are a few unusual differences that often show up in medieval texts (mostly spelling, but also some grammar, like introducing a relative clause with "quod" rather than using an accusative-infinitive construction, the way Romance languages had evolved).

For me, for the crusades and medieval law, almost everything is in Latin. But what about my friends who studied Middle English, or Old Irish, or Middle Welsh, or Old Church Slavonic? Not everyone actually needs Latin to study the Middle Ages. But those were the rules, everyone had to pass the Latin exams, and if they didn't pass they would get kicked out of the program.

We were also expected (although it wasn't mandatory) to take any other language classes that might be useful in our future careers. I took Old French and Arabic, other students took Italian, or Greek, or Hebrew, or Old Norse - there were plenty of options available.

Ancient Greek would have been extremely useful for me, since medieval Greek is very similar. Unfortunately I just never got around to it.

The answer will be different for every field of history and maybe even for every school. Latin is the most important language for me, and ancient Greek would have been useful too. But some historians might never have to learn another language at all, nevermind Latin or Greek.

PhD in Classical Archaeology here. It depends a lot on what kind of historical research you mean. All the major ancient texts are available in translation.

Both Greek and Latin are delightful but only really necessary if you are doing professional work on the ancient Mediterranean or early medieval Europe. Even then, you will use French, German or Italian just as much (or more) in order to read the relevant scholarship.