Spatially resolved stellar populations of massive quiescent galaxies at cosmic noon provide powerful insights into star-formation quenching and stellar mass assembly mechanisms. Previous photometric studies have revealed that the cores of these galaxies are redder than their outskirts. However, spectroscopy is needed to break the age-metallicity degeneracy and uncover the driver of these colour gradients. In this work, we derive the age and elemental abundance gradients for eight distant (1.2 ≲ z ≲ 2.2), massive (10.3 ≲ log(M*/M⊙)≲11.1) quiescent galaxies by fitting full-spectrum models to ultra-deep NIRSpec-MSA spectroscopy from the JWST-SUSPENSE survey. We find that these galaxies have negative age and flat [Fe/H] gradients as well as tentative indications of positive [Mg/H] and [Mg/Fe] gradients. These results suggest that galaxy cores are older and perhaps also Mg deficient compared to galaxy outskirts. The age gradients may indicate inside-out quenching, while Mg-deficient cores could suggest rapid gas expulsion as the central quenching mechanism. Thus, galaxy cores may have formed faster and quenched more efficiently than their outskirts. In this scenario, however, our [Fe/H] and [Mg/Fe] gradients are still puzzling, and further investigation is required to understand the nature of [Mg/H] gradients in massive quiescent galaxies at these redshifts. Our results contrast with those of lower-redshift studies, which find flat age and [Mg/Fe] gradients and negative metallicity gradients. Additionally, we find a positive trend between age gradients and rotational support and marginal trends between [Fe/H] gradients and galaxy velocity dispersions and ages. We discuss our findings in the context of galaxy growth scenarios, including minor mergers and progenitor bias. With this work, we present the first stellar population gradients from NIRSpec-MSA spectroscopy in the current largest sample of distant quiescent galaxies.