In the field of high performance computing, massively-parallel many-core processors such as Intel Xeon Phi coprocessors are becoming popular because they can significantly accelerate various applications. In order to efficiently parallelize applications for such many-core processors, several high-level programming models have been proposed. The de facto standard programming model mainly for shared-memory parallel processing is OpenMP. For hierarchical parallel processing, OpenMP version 4.0 or later allows programmers to create multiple thread teams. Each thread team contains a bunch of newly-created synchronizable threads. When multiple thread teams are used to execute an application, it is important to have dynamic load balancing across thread teams, since static load balancing easily encounters load imbalance across teams, and thus degrades performance. In this paper, we first motivate our work by clarifying the benefit of using multiple thread teams to execute an irregular workload on a many-core processor. Then, we demonstrate that dynamic load balancing across those thread teams has a potential of significantly improving the performance of irregular workloads on a many-core processor, with considering the scheduling overhead. Although such a dynamic load balancing mechanism has not been provided by the current OpenMP specification, the benefits of dynamic load balancing across thread teams are discussed through experiments using the Intel Xeon Phi coprocessor. We evaluate the performance gain of dynamic load balancing across thread teams using a ray tracing code. The results show that such a dynamic load balancing mechanism can improve the Toward Dynamic Load Balancing across OpenMP Thread Teams for Irregular Workloads performance by up to 14% compared to static load balancing across teams, with considering scheduling overhead.