  This work includes a comprehensive analysis of the Kepler detached eclipsing
binary system KIC 6629588 that aims to the detailed study of the oscillation
properties of its pulsating component. Ground-based spectroscopic observations
were obtained and used to classify the components of the system. The
spectroscopic results were used as constrains for the modelling of the
short-cadence Kepler light curves and for the estimation of the absolute
parameters of the components. Furthermore, the light curves residuals are
analyzed using Fourier transformation techniques in order to search for
pulsation frequencies. The primary component of the system is identified as a
$\delta$ Scuti star that pulsates in seven eigenfrequencies in the range 13-22
d$^{-1}$, while more than 270 combination frequencies were also detected. The
absolute and the oscillation parameters of this pulsating star are compared
with those of other $\delta$ Scuti stars-members of detached binary systems
using evolutionary and correlation diagrams. Finally, the distance of the
system is also estimated.
