In plain English
FAR 52.207-3, Right of First Refusal of Employment, is a contract clause prescribed at FAR 7.305(c), most recently dated May 2006. The complete official text is reproduced below, verbatim, from GSA's published FAR source files.
Its text contains no sentence requiring insertion into subcontracts; see the flowdown section below for what that does and does not mean.
Does it flow down to subcontracts?
No flowdown mandate found in the clause text
We scanned the full clause text and found no sentence directing the contractor to insert this clause into subcontracts. That is a statement about the text, not legal advice: a prime contractor may still flow terms down contractually, an agency supplement (DFARS, VAAR, …) may add requirements, and clauses listed below (if any) may order this clause into subcontracts from the outside.
Where it's prescribed
As prescribed in 7.305(c), insert the following clause:
Prescribing reference: FAR 7.305(c).
The official text, verbatim
As prescribed in 7.305(c), insert the following clause:
Right of First Refusal of Employment (May 2006)
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(a) The Contractor shall give Government personnel who have been or will be adversely affected or separated as a result of award of this contract the right of first refusal for employment openings under the contract in positions for which they are qualified, if that employment is consistent with post-Government employment conflict of interest standards.
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(b) Within 10 days after contract award, the Contracting Officer will provide to the Contractor a list of all Government personnel who have been or will be adversely affected or separated as a result of award of this contract.
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(c) The Contractor shall report to the Contracting Officer the names of individuals identified on the list who are hired within 90 days after contract performance begins. This report shall be forwarded within 120 days after contract performance begins.
(End of clause)