[en] In the absence of efficient collisions, deviations from thermal equilibrium of plasma particle distributions are controlled by the self-generated instabilities. The whistler instability is a notorious example, usually responsible for the regulation of electron temperature anisotropy $A=T_{\perp <!--\; ???\; -->}/T_{\parallel <!--\; ???\; -->}>1$ (with $\perp <!--\; ???\; -->,\parallel <!--\; ???\; -->$ respective to the magnetic field direction) observed in space plasmas, e.g., solar wind and planetary magnetospheres. Suprathermal electrons present in these environments change the plasma dispersion and stability properties, with expected consequences on the kinetic instabilities and the resulting fluctuations, which, in turn, scatter the electrons and reduce their anisotropy. In order to capture these mutual effects we use a quasilinear kinetic approach and PIC simulations, which provide a comprehensive characterization of the whistler instability under the influence of suprathermal electrons. Analysis is performed for a large variety of plasma conditions, ranging from low-beta plasmas encountered in outer corona or planetary magnetospheres to a high-beta solar wind characteristic to large heliospheric distances. Enhanced by the suprathermal electrons, whistler fluctuations stimulate the relaxation of temperature anisotropy, and this influence of suprathermals increases with plasma beta parameter.