In this work, we introduce a time-like ruled surface in one-parameter hyperbolic dual spherical motions. This provides the ability
to derive some formulae of surface theory into line spaces. Then, a time-like Plücker conoid associated with the motion has been
obtained, and its kinematic geometry is researched in detail. Consequently, a characterization for a time-like ruled surface to be a
constant Disteli-axis is derived and investigated in detail. At last, we have discussed some special cases which lead to some special
time-like ruled surfaces such as the time-like helicoids, Lorentzian sphere, and time-like cone.