ABSTRACT We predict the non-thermal pressure (NTP) induced in the cores of galaxy clusters by kinetic jet feedback from an active galactic nucleus (AGN). We model a population of Fanaroff–Riley type I jets when sampling power-law distributions in jet power and age, which we evolve in time with a two-phase jet-lobe model. We couple the energy of each jet outburst to the surrounding gas inside spherical shells, allowing us to estimate the fraction of NTP to total pressure induced in the cluster. We predict the mean profile for this NTP fraction over the source population in a variety of cluster environments and for different AGN jet duty cycles. For typical gas and dark matter profiles, the mean NTP fraction peaks at $\sim ~4\!-\!6{{\ \rm per\ cent}}$ when the AGN jets are active for $10\!-\!30~{{\rm per\ cent}}$ of the total AGN lifecycle. These predictions are in good agreement with observational constraints, suggesting that AGN feedback imparts only small non-thermal contributions to the cluster’s core. Furthermore, we find a relationship between the peak in the mean NTP fraction and the AGN jet duty cycle in a given cluster environment. Applying this to Hitomi measurements of the NTP in the Perseus cluster, we infer an AGN jet duty cycle that is consistent with independent evidence of Perseus’ AGN jet activity. We propose this as a novel approach for observationally inferring the past AGN activity of real clusters from their observed NTP fraction and environmental profiles.