The paradigm of extracting work from an isolated quantum system through a cyclic Hamiltonian process is a topic of immense research interest. The optimal work extracted under such a process is termed ergotropy [Europhys. Lett. 67, 565 (2004)]. Here, in a multiparty scenario, we consider only a class of such cyclic processes that can be implemented locally, giving rise to the concept of local ergotropy. Eventually, the presence of quantum correlations results in a nonvanishing thermodynamic quantity called an ergotropic gap, measured by the difference between global and local ergotropy. However, the converse does not hold in general, i.e., its nonzero value does not necessarily imply the presence of quantum correlations. For arbitrary multiparty states, we quantify this gap. We also evaluate the difference between maximum global and local extractable work for arbitrary states when the system is no longer isolated but put in contact with a bath of the same local temperature.