  The motion of the barycenter of the Solar System (SSB), the origin of the
International Celestial Reference System, causes a directional displacement
known as secular aberration. The secular aberration drift caused by the
galactocentric acceleration of the SSB has been modeled in the third generation
of the International Celestial Reference Frame. We aim to address another
secular aberration drift effect due to the change in the line-of-sight
direction and study its implications for stellar proper motions. A complete
formula of secular aberration drift is derived, and its influence on stellar
proper motion is computed based on the astrometric data in \textit{Gaia} Data
Release 3. We found that the secular aberration drift due to the change in the
line-of-sight direction tends to decrease the observed proper motions for stars
with galactic longitudes between $0^{\circ}$ and $180^{\circ}$, and increase
the observed proper motion for stars in the remaining region. If this secular
aberration drift effect is ignored, it will induce an additional proper motion
of $>1\,\mathrm{mas\,yr^{-1}}$ for 84 stars and $>0.02\,\mathrm{mas\,yr^{-1}}$
for 5\,944\,879 stars, which is comparable to or several times greater than the
typical formal uncertainty of the \textit{Gaia} proper motion measurements at
$G<13$. The secular aberration drift due to the change in the line-of-sight
direction and the acceleration of the SSB should be modeled to make the stellar
reference frame consistent with the extragalactic reference frame.
