In the coming decades, the next set of great observatories will begin to explore the atmospheres of temperate, rocky exoplanets. In this new era, knowledge of the UV radiation of exoplanet host stars, across wavelength and time, will be critical to interpreting the atmospheric spectra of these exoplanets. Because UV photons participate heavily in atmospheric chemistry, without this knowledge it is impossible to untangle the role of photochemistry from geochemistry and, perhaps, biochemistry, in establishing a planet’s atmospheric composition. Resolving this ambiguity requires monitoring the variable, often volatile, UV emission of the planetary host star. Because observing a single star in every conceivable activity state is impossible, this monitoring must be buttressed with a legacy dataset of stellar UV spectra across rotational phases, long-term activity cycles, flaring states, spectral types, and ages. This requires a space-borne UV spectrograph that, unlike HST, has the freedom to stare, accumulating a more time-complete characterization of stellar UV radiation that previously possible. Here, we will explain why time-domain UV spectroscopy is essential to answering anticipated questions regarding the source of molecules we expect future telescopes will observe in rocky-planet atmospheres, and how a new Medium-Class Explorer mission concept, UV-SCOPE (Ultraviolet Spectroscopic Characterization of Planets and their Environments), could serve this key role in the search for life beyond the Solar System.