  We study the $\delta$ Scuti -- red giant binary KIC9773821, the first
double-pulsator binary of its kind. It was observed by \textit{Kepler} during
its four-year mission. Our aims are to ascertain whether the system is bound,
rather than a chance alignment, and to identify the evolutionary state of the
red giant via asteroseismology. An extension of these aims is to determine a
dynamical mass and an age prior for a $\delta$ Sct star, which may permit mode
identification via further asteroseismic modelling. We determine spectroscopic
parameters and radial velocities (RVs) for the red giant component using
HERMES@Mercator spectroscopy. Light arrival-time delays from the $\delta$ Sct
pulsations are used with the red-giant RVs to determine that the system is
bound and to infer its orbital parameters, including the binary mass ratio. We
use asteroseismology to model the individual frequencies of the red giant to
give a mass of $2.10^{+0.20}_{-0.10}$ M$_{\odot}$ and an age of
$1.08^{+0.06}_{-0.24}$ Gyr. We find that it is a helium-burning secondary clump
star, confirm that it follows the standard $\nu_{\rm max}$ scaling relation,
and confirm its observed period spacings match their theoretical counterparts
in the modelling code MESA. Our results also constrain the mass and age of the
$\delta$ Sct star. We leverage these constraints to construct $\delta$ Sct
models in a reduced parameter space and identify four of its five pulsation
modes.
