extended warranty
A service contract that prolongs the warranty period beyond the standard coverage, common for electronics and appliances.
You can add an extended warranty to this TV.
If you sign up for the extended warranty, repair costs will be free.
保証 is a general warranty or guarantee, while 延長保証 specifically refers to an extension of that warranty period.
メーカー保証 is the manufacturer's standard warranty, whereas 延長保証 is an optional extension beyond that.
Compound of 延長 (extension) and 保証 (warranty). A straightforward modern term with no obscure historical derivation.