A new trend in topic modeling research is to do Neural Topic Modeling by Clustering document Embeddings (NTM-CE) created with a pretrained language model. Studies have evaluated static NTM-CE models and found them performing comparably to, or even better than other topic models. An important extension of static topic modeling is making the models dynamic, allowing the study of topic evolution over time, as well as detecting emerging and disappearing topics. In this research proposal, we present two research questions to understand dynamic topic modeling with NTM-CE theoretically and practically. To answer these, we propose four phases with the aim of establishing evaluation methods for dynamic topic modeling, finding NTM-CE-specific properties, and creating a framework for dynamic NTM-CE. For evaluation, we propose to use both quantitative measurements of coherence and human evaluation supported by our recently developed tool.