An example of a clock that would not experience time dilation is a clock that is stationary relative to an observer. Time dilation occurs when there is relative motion between two objects or when they are in different gravitational fields.
If a clock is stationary with respect to an observer, meaning it is not moving relative to the observer and is located in the same gravitational field, then it would not experience time dilation. In this case, the clock and the observer would share the same reference frame, and time would flow at the same rate for both of them.
For example, if you have a clock sitting on a table in a stationary room, and an observer is also at rest in the same room, the clock and the observer will experience time passing at the same rate. There would be no relative motion or gravitational differences to cause time dilation between the clock and the observer in this scenario.