How can I tell if I need a better clock for my DAC?

In layman’s terms, you are referring to jitter correction. Jitter refers to the timing of the data stream (bits, or 0’s and 1’s) and insuring that they all arrive at the same time for processing. The Synchro-mesh and related products insure this correct timing plus can reject noise.

No CDP is jitter-free. The design and implementation will determine how well a standalone component or dac/transport will correct jitter. A manufacturer is also dealing with a price point of the component which includes the quality of electronics, vibration control of the transport, the power supply, and function of the laser.

Other members, including Steve N. (audioeng) can explain jitter correction in detail. Steve can explain measuring jitter since that’s what he does.
I thought I might start things off with the basics since it is complicated subject matter.

Clocking before the DAC can make a huge difference.

Agree. I use a PS Audio PWT transport which, as many of you know, reads the CD and loads it into a buffer. It then clocks the data and sends out a timed bitstream to an external DAC.
This is why a good cable is needed to preserve the reduced jitter signal.