Systems that adapt to their environment or change based on new requirements pose challenges for runtime verification. Complexity is increased when the system needs to retain its internal state and continue monitoring while also updating properties or adding new ones during runtime. In this work, we propose DynSRV, a Stream Runtime Verification language that allows for dynamic updates of properties. A core benefit of this language is its capability to update properties at runtime without requiring a restart of the monitor, maintaining the internal state of the remaining properties. We formalise the semantics of our core primitives and demonstrate design patterns for allowing adaptations under certain constraints. Finally, we present an implementation of DynSRV and describe three memory strategies that balance memory usage and the ability to resolve dynamically added properties depending on historical data.