Can the new organization compete a task order to have the work performed or is the work now considered a "new start" and there are no "new starts under a CR?
This response is based on the information provided. We suggest you discuss with your contracting team, program manager and/or legal department as appropriate.
A Continuing Resolution (CR) doesn't allow for new work as you have noted. The focus of the prohibition of new work is related to the work itself, not what organization is having it done. If the work to be done was being done and is continuing for the same purpose then the organization acquiring it does not affect the determination of continuing necessary work.