This game is to practice relative pronouns after the students are familiar with them. I swiped it from an observation class I watched a couple years ago, but it's probably a fairly common activity. Here's my take on it:
First, I write three hints on the blackboard that are about a teacher at the school. For example...
Then I ask the JTE or the students to guess who it is. Once they have the correct answer, I give another example or two but I just speak them. Once the students have the general idea of the activity, I put them into groups of about 4 or 5 and ask them to come up with their own examples - two teachers and one student. As they're writing, I try and write some examples of verbs up on the blackboard that they might find useful ("has..." "looks like..." "goes to..." "says...").
Depending on how advanced the class is and how familiar they are with the grammar, it might take them a while to come up with the three examples. Once all the groups are most of the way there, you can have the students start giving their quizzes to each other. In the past I would number the groups, have each group choose a representative, and have them read it off to the full class, who can either raise their hands or write their answers on a small whiteboard if they have them. Recently I've just been asking the students to stand up and give their quizzes to other students individually, since it gives students more speaking practice. Go with whatever format works well for your situation!
You can do this activity with other grammar points, but I like to do it for relative pronouns since it reinforces that relative pronouns are a good tool for explaining people and things. If the students are likely to be unkind to another student in class, you can make a rule that the student can't be one of the students in the current class. The students usually think of pretty funny things to say about their teachers, so in my experience they enjoy this activity a lot.