When forming a team or group of individuals, we often seek a balance of expertise in a particular task while at the same time maintaining diversity of skills within each group. Here, we view the problem of finding diverse and experienced groups as clustering in hypergraphs with multiple edge types. The input data is a hypergraph with multiple hyperedge types -- representing information about past experiences of groups of individuals -- and the output is groups of nodes. In contrast to related problems on fair or balanced clustering, we model diversity in terms of variety of past experience (instead of, e.g., protected attributes), with a goal of forming groups that have both experience and diversity with respect to participation in edge types. In other words, both diversity and experience are measured from the types of the hyperedges. Our clustering model is based on a regularized version of an edge-based hypergraph clustering objective, and we also show how naive objectives actually have no diversity-experience tradeoff. Although our objective function is NP-hard to optimize, we design an efficient 2-approximation algorithm and also show how to compute bounds for the regularization hyperparameter that lead to meaningful diversity-experience tradeoffs. We demonstrate an application of this framework in online review platforms, where the goal is to curate sets of user reviews for a product type. In this context, "experience" corresponds to users familiar with the type of product, and "diversity" to users that have reviewed related products.