In plain English
FAR 52.211-13, Time Extensions, is a contract clause prescribed at FAR 11.503(c), most recently dated Sept 2000. 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 11.503(c), insert the following clause:
Prescribing reference: FAR 11.503(c).
The official text, verbatim
As prescribed in 11.503(c), insert the following clause:
Time Extensions (Sept 2000)
Time extensions for contract changes will depend upon the extent, if any, by which the changes cause delay in the completion of the various elements of construction. The change order granting the time extension may provide that the contract completion date will be extended only for those specific elements related to the changed work and that the remaining contract completion dates for all other portions of the work will not be altered. The change order also may provide an equitable readjustment of liquidated damages under the new completion schedule.
(End of clause)