In plain English
FAR 52.217-9, Option to Extend the Term of the Contract, is a contract clause prescribed at FAR 17.208(g), most recently dated Mar 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 17.208(g), insert a clause substantially the same as the following:
Prescribing reference: FAR 17.208(g).
The official text, verbatim
As prescribed in 17.208(g), insert a clause substantially the same as the following:
Option to Extend the Term of the Contract (Mar 2000)
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(a) The Government may extend the term of this contract by written notice to the Contractor within _____ [insert the period of time within which the Contracting Officer may exercise the option]; provided that the Government gives the Contractor a preliminary written notice of its intent to extend at least _____ days[60days unless a different number of days is inserted] before the contract expires. The preliminary notice does not commit the Government to an extension.
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(b) If the Government exercises this option, the extended contract shall be considered to include this option clause.
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(c) The total duration of this contract, including the exercise of any options under this clause, shall not exceed ___________ (months) (years).
(End of clause)