The element abundances in the solar corona and solar wind are often different from those of the solar photosphere, typically with a relative enrichment of elements with low first ionization potential (FIP effect). Here, we study the spatial distribution and temporal evolution of the coronal chemical composition in an active region (AR) over about 10 days, using Hinode/EIS spectra, and we also analyze coordinated IRIS observations of the chromospheric and transition region emission to investigate any evidence of the footprints of the FIP effect in the lower atmosphere. To derive the coronal abundances, we use a spectral inversion method recently developed for the MUSE investigation. We find that, in the studied active region (AR 12738), the coronal FIP bias, as diagnosed by the Si/S abundance ratio, presents significant spatial variations, with its highest values (∼2.5–3.5) in the outflow regions at the boundary of the AR, but typically modest temporal variability. Some moss regions and some regions around the AR sunspot show enhanced FIP bias (∼2–2.5) with respect to the AR core, which has only a small FIP bias of ∼1.5. The FIP bias appears most variable in these moss regions. The IRIS observations reveal that the chromospheric turbulence, as derived from IRIS2 inversions of the Mg ii spectra, is enhanced in the outflow regions characterized by the high FIP bias, providing significant new constraints to both models aimed at explaining the formation of AR outflows and models of chemical fractionation.