Marine protected areas (MPAs) have become an increasingly important tool to protect and conserve marine resources. However, there remains much debate about how effective MPAs are, especially in terms of their ability to protect mobile marine species such as teleost and chondrichthyan fishes. We used satellite and acoustic tags to assess the ability of a large oceanic MPA, the British Indian Ocean Territory MPA (BIOT MPA), to protect seven species of pelagic and reef-associated teleost and chondrichthyan fishes. We satellite-tagged 26 animals from six species (Blue Marlin, Reef Mantas, Sailfish, Silky Sharks, Silvertip Sharks, and Yellowfin Tuna), producing 2,735 days of movement data. We also acoustically tagged 121 sharks from two species (Grey Reef and Silvertip Sharks), which were monitored for up to 40 months across a large acoustic receiver array spanning the MPA. We found that the activity spaces of all satellite-tagged animals, including pelagic species, were much smaller than the area of the BIOT MPA, even taking into account errors associated with position estimates. Estimates of space use of acoustically tagged sharks, based on dynamic Brownian Bridge Movement Models (dBBMM), were also much smaller than the size of the MPA. However, we found important limitations when using dBBMM and demonstrate its sensitivity to both study duration and array design. We found that Grey Reef Sharks should be monitored for at least 1 year and Silvertip Sharks for 2 years before their activity space can be effectively estimated. We also demonstrate the potentially important role that intraspecific variability in spatial ecology may play in influencing the ability of MPAs to effectively protect populations of mobile species. Overall, our results suggest that, with effective enforcement, MPAs on the scale of the BIOT MPA potentially offer protection to a variety of pelagic and reef species with a range of spatial ecologies. We suggest that animals need to be tagged across seasons, years, and ontogenetic stages, in order to fully characterize their spatial ecology, which is fundamental to developing and implementing effective MPAs to conserve the full life history of target species.