  This work presents accurate {\it ab initio} determination of the magnetic
dipole (M1) and electric quadrupole (E2) hyperfine structure constants for the
ground and a few low-lying excited states in $^{67}$Zn$^{+}$, which is one of
the interesting systems in fundamental physics. The coupled-cluster (CC) theory
within the relativistic framework has been used here in this calculations. Long
standing demands for a relativistic and highly correlated calculations like CC
can be able to resolve the disagreements among the lifetime estimations
reported previously for a few low-lying states of Zn$^{+}$. The role of
different electron correlation effects in the determination of these quantities
are discussed and their contributions are presented.
