  We investigated for a possible connection between the types of X-ray binaries
(XRBs) and the properties of compact star clusters in the nearby galaxy NGC
628. Using {\it Chandra} archival data covering the years 2001-2018, 75 X-ray
sources were detected within the field of view of observations. A total of 69
XRBs, one of which is an ultraluminous X-ray source (ULX), were found to be in
the luminosity range of 3$\times10^{36}\leq L_{X}$ $\leq $ 2$\times10^{39}$ erg
s$^{-1}$. We identified the optical counterpart(s) of 15 of the 42 XRBs that
coincide with the {\it HST} field of view via improved astrometry. We
classified 15 of them as HMXBs based on the presence of the optical
counterparts. The remaining sources with no optical counterparts were
classified as LMXBs. We also search compact star clusters in this galaxy using
the multi-band optical images drawn from {\it HST} archives. 864 compact star
clusters were identified and their ages and masses were determined by applying
the best-fit SSP (Simple Stellar Population) model to their color-color
diagram. We found that in NGC 628, HMXBs are associated with younger star
clusters and LMXBs with older ones. Our findings support a connection between
different types of XRBs and cluster ages, already known to exist for other
galaxies.
