When we try to define time, we define it based on an event which happens periodically. For example, in a clock,we say that the time elapsed is 1 minute if the second hand completes 1 revolution. Here we define time based on the periodic motion of the second hand. From Wikipedia, Motion is defined as:
Motion is a change in position of an object with respect to time
Here we are trying to define time based on motion which is in turn based on time. So the question is - does time exist in reality?