In plain English
FAR 52.247-21, Contractor Liability for Personal Injury and/or Property Damage, is a contract clause prescribed at FAR 47.207-7(c), most recently dated Apr 1984. 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 47.207-7(c), insert the following clause in solicitations and contracts for transportation or for transportation-related services:
Prescribing reference: FAR 47.207-7(c).
The official text, verbatim
As prescribed in 47.207-7(c), insert the following clause in solicitations and contracts for transportation or for transportation-related services:
Contractor Liability for Personal Injury and/or Property Damage (Apr 1984)
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(a) The Contractor assumes responsibility for all damage or injury to persons or property occasioned through the use, maintenance, and operation of the Contractor’s vehicles or other equipment by, or the action of, the Contractor or the Contractor’s employees and agents.
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(b) The Contractor, at the Contractor’s expense, shall maintain adequate public liability and property damage insurance during the continuance of this contract, insuring the Contractor against all claims for injury or damage.
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(c) The Contractor shall maintain Workers’ Compensation and other legally required insurance with respect to the Contractor’s own employees and agents.
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(d) The Government shall in no event be liable or responsible for damage or injury to any person or property occasioned through the use, maintenance, or operation of any vehicle or other equipment by, or the action of, the Contractor or the Contractor’s employees and agents in performing under this contract, and the Government shall be indemnified and saved harmless against claims for damage or injury in such cases.
(End of clause)