  We find a characteristic low-energy peak structure located in the range of
100-300 cm$^{-1}$ in the optical conductivity spectra of a
quasi-two-dimensional organic compound with a triangular lattice,
${\theta}$-$\mbox{(BEDT-TTF)}_2\mbox{CsZn(SCN)}_4$, in which two different
types of short-range charge orderings (COs) coexist. Upon lowering the
temperature, the low-energy peak becomes significant and shifts to much lower
frequencies only for the polarization of ${E \parallel a}$, in contrast to the
other broad electronic bands in the mid-infrared region. On introducing
disorder, the low-energy peak is strongly suppressed in comparison with the
broad electronic bands. This result indicates that the low-energy peak is
attributed to a collective excitation that originates from the short-range CO
with a relatively long-period $3\times3$ pattern. The present results shed
light on the understanding of the low-energy excitation in the glassy
electronic state, where the charge degrees of freedom remain at low
temperatures.
