Trends in population sizes influence conservation decisions, but such trends can be misleading since a population can grow even as carrying capacity falls. Population growth requires population size to be below carrying capacity but is agnostic to trends in carrying capacity. We developed an approach to estimate time-varying carrying capacity (Kt), an integrative metric to monitor all environmental variables impacting vital rates in a population. We used individual-based modelling to quantify Kt for a recovering population of spotted hyenas and investigated whether population growth could be explained by recent environmental change. Population growth occurred despite no linear trend in Kt, suggesting that the observed growth is the lingering effect of past, rather than recent, environmental improvements. This study illustrates that recovery can occur at different time scales for the environment and for a population. Considering this demographic lag matters for the effective conservation of long-lived species.