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Multiwinner voting is the study of electing a fixed-size committee given individual agents' preferences over candidates. Most research in this field has been limited to a static setting, with only one election over a fixed set of candidates. However, this approach overlooks the dynamic nature of applications, where candidate sets are subject to change.We extend the study of proportionality in multiwinner voting to dynamic settings, allowing candidates to join or leave the election and demanding that each chosen committee satisfies proportionality without differing too much from the previously selected committee. We consider approval preferences, ranked preferences, and the proportional clustering setting. In these settings, we either give algorithms making few changes or show that such algorithms cannot exist for various proportionality axioms. In particular, we show that such algorithms cannot exist for ranked preferences and provide amortized and exact algorithms for several proportionality notions in the other two settings.