Chromatin remodeling is central to the dynamic changes in gene expression that drive cell fate determination. During development, the sets of enhancers that are accessible for use change globally as cells transition between stages. While transcription factors and nucleosome remodelers are known to work together to control enhancer accessibility, it is unclear how the short stretches of DNA that they individually unmask yield the kilobase-sized accessible regions characteristic of active enhancers. Here, we performed a genetic screen to investigate the role of nucleosome remodelers in control of dynamic enhancer activity. We find that the Drosophila Switch/Sucrose Non-Fermenting complex, BAP, is required for repression of a temporally dynamic enhancer, brdisc. Contrary to expectations, we find that the BAP-specific subunit Osa is dispensable for mediating changes in chromatin accessibility between the early and late stages of wing development. Instead, we find that Osa is required to constrain the levels of brdisc activity when the enhancer is normally active. Genome-wide profiling reveals that Osa directly binds brdisc as well as thousands of other developmentally dynamic regulatory sites, including multiple genes encoding components and targets of the Notch signaling pathway. Transgenic reporter analyses demonstrate that Osa is required for activation and for constraint of different sets of target enhancers in the same cells. Moreover, Osa loss results in hyperactivation of the Notch ligand Delta and development of ectopic sensory structures patterned by Notch signaling early in development. Together, these findings indicate that proper constraint of enhancer activity is necessary for regulation of dose-dependent developmental events.