I'm not sure about the timing window on trace effects, so my question is if it is possible to use a Clone Chip to bring back a Disrupter to prevent and re-initiate a trace? Are there different rules regarding where the trace came from e.g is it possible to Clone Chip a Disrupter against an operation (SEA Source, Punitive Counterstrike, etc.) or an Upgrade (Bernice Mai, Ash, etc.)? What if I use a Disrupter on a 1st trace, but a 2nd trace attempt comes up, can I Clone Chip that same Disrupter?

Short answer: Nope.

Long answer: Only Prevent or Avoid effects can interrupt another effect's resolution. Although Disruptor IS a Prevent effect, Clone Chip is not, and so cannot be played once the Corp begins a trace. You'd need to have Disruptor already installed.

EDIT: If you can see a trace coming but it hasn't yet begun to resolve (such as when you're approaching a piece of ICE), as long as there is a Paid Ability window, you can Clone Chip away - just be sure and check the timing chart for when Paid Abilities are legal.