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We present a new study of the Algol-type eclipsing binary system AS Eri based on the combination of the MOST and TESS light curves and a collection of very precise radial velocities obtained with the spectrographs HERMES operating at the Mercator telescope, La Palma, and TCES operating at the Alfred Jensch telescope, Tautenburg. The primary component is an A3 V-type pulsating, mass-accreting star. We fitted the light and velocity data with the package PHOEBE, and determined the best-fitting model adopting the configuration of a semi-detached system. The orbital period has been improved using a recent (O-C) analysis and the phase shift detected between both light curves to the value 2.6641496 $\pm$ 0.0000001 days. The absence of any cyclic variation in the (O-C) residuals confirms the long-term stability of the orbital period. Furthermore, we show that the models derived for each light curve separately entail small differences, e.g. in the temperature parameter T$_{\rm eff,2}$. The high quality of the new solutions is illustrated by the residuals. We obtained the following absolute component parameters: L$_1$ = 14.125~L$_{\odot}$, M$_1$ = 2.014~M$_{\odot}$, R$_1$ = 1.733~R$_{\odot}$, log g$_1$ = 4.264, L$_2$ = 4.345~L$_{\odot}$, M$_2$ = 0.211~M$_{\odot}$, R$_2$ = 2.19~R$_{\odot}$, log g$_2$ = 3.078~ with T$_{\rm eff,2}$/T$_{\rm eff,1}$ = 0.662 $\pm$ 0.002. Although the orbital period appears to be stable on the long term, we show that the light-curve shape is affected by a years-long modulation which is most probably due to the magnetic activity of the cool companion.