Excited states in the neutron-rich 121, 123, 125Ag were studied via the fragmentation of a 136Xe beam at 120MeV/nucleon in a thick 9Be target. The levels in 121Ag were populated in the β decay of 121Pd while those assigned to 123, 125Ag were identified via isomer spectroscopy. The transitions identified in 121Ag are consistent with the γ-rays reported in 117, 119Ag. The newly observed transitions were placed in the level schemes of 123, 125Ag based on the analysis of γ-γ coincidences and the systematics. We attribute the onset of isomerism in the 123, 125Ag isotopes to the drop in energy of the negative-parity levels similar to the 5- state in the even-even Cd cores. The proposed level scheme for 125Ag is well described by the NuShellX shell model calculations.