  We present a novel approach to measuring the expansion rate and the geometry
of the Universe, which combine time-delay cosmography in lens galaxy clusters
with pure samples of 'cosmic chronometers' (CCs) by probing the member
galaxies. The former makes use of the measured time delays between the multiple
images of time-varying sources strongly lensed by galaxy clusters, while the
latter exploits the most massive and passive cluster member galaxies to measure
the differential time evolution of the Universe. We applied two different
statistical techniques, adopting realistic errors on the measured quantities,
to assess the accuracy and the gain in precision on the values of the
cosmological parameters. We demonstrate that the proposed combined method
allows for a robust and accurate measurement of the value of the Hubble
constant. In addition, this provides valuable information on the other
cosmological parameters thanks to the complementarity between the two different
probes in breaking parameter degeneracies. Finally, we showcase the immediate
observational feasibility of the proposed joint method by taking advantage of
the existing high-quality spectro-photometric data for several lens galaxy
clusters.
