  The advancement of astronomical observations opens the possibility of testing
our current understanding of gravitational theory in the strong-field regime
and probing any deviation from general relativity. We explore to what extent
compact stars predicted by non-minimal derivative coupling (NMDC) gravity
theory agree with observed data. We investigate white dwarfs (WDs), neutron
stars (NSs), and quark stars (QSs) mass and radius in various values of
constant scalar $|Q_{\infty}|$ at coupling strength of $\eta=\pm1$. This study
focuses on the astrophysical impacts of altering maximum masses by values of
$|Q_{\infty}|$ and $\eta$. From an observational point of view, we found that
WD stars are consistent with ultra-cold WD data at $|Q_{\infty}| \lesssim 0.2$.
We also found that QS has a similar impact of mass-radius to NS, where the
modification is more significant at higher (central) density. For NS and QS
EoSs, the value $|Q_{\infty}|$ strongly alters the critical mass and might
eliminate the $M-\rho_c$ turning point in the negative $\eta$ case. In that
case, the sufficiently large $|Q_{\infty}|$ could predict $M>2.6 M_\odot$ NS
and QS, i.e., larger than GW190814 secondary counterpart. We suggest that the
lower mass gap in the gravitational wave and x-ray binary mass population data
might restrict the theory's $|Q_{\infty}|$.
