Passive early-type galaxies dominate cluster cores at z \lesssim 1.5 . At higher redshift , cluster core galaxies are observed to have still on-going star-formation , fuelled by cold molecular gas . We measure the molecular gas reservoir of the central region around the radio-loud AGN in the cluster CARLA J1103+3449 at z = 1.44 with NOEMA . The AGN synchrotron emission dominates the continuum emission at 94.48 GHz , and we measure its flux at the AGN position and at the position of two radio jets . Combining our measurements with published results over the range 4.71 GHz-94.5 GHz , and assuming S _ { synch } \propto \nu ^ { - \alpha } , we obtain a flat spectral index \alpha = 0.14 \pm 0.03 for the AGN core emission , and a steeper index \alpha = 1.43 \pm 0.04 and \alpha = 1.15 \pm 0.04 at positions close to the western and eastern lobe , respectively . The total spectral index is \alpha = 0.92 \pm 0.02 over the range 73.8 MHz-94.5 GHz . We detect two CO ( 2-1 ) emission lines , both blue-shifted with respect to the AGN . Their emission corresponds to two regions , \sim 17 kpc south-east and \sim 14 kpc south-west of the AGN , not associated with galaxies . In these two regions , we find a total massive molecular gas reservoir of M ^ { tot } _ { gas } = 3.9 \pm 0.4 \times 10 ^ { 10 } M _ { \astrosun } , which dominates ( \gtrsim 60 \% ) the central total molecular gas reservoir . These results can be explained by massive cool gas flows in the center of the cluster . The AGN early-type host is not yet quenched ; its star formation rate is consistent with being on the main sequence of star-forming galaxies in the field ( SFR \approx 30 - 140 M _ { \astrosun } { yr ^ { -1 } } ) , and the cluster core molecular gas reservoir is expected to feed the AGN and the host star-formation before quiescence . The other cluster confirmed members show star formation rates at \sim 2 \sigma below the field main sequence at similar redshifts and do not have molecular gas masses larger than galaxies of similar stellar mass in the field .