Renew

An extension of the period for which a book or other item is loaned by a library, usually by the length of the normal borrowing period. Renewal policies vary, but most libraries allow at least one renewal. To avoid fines, material must be renewed on or before the due date. Branches may prohibit renewals if another patron has placed a hold, so an item can get to the next person quickly. Particularly in academic libraries, borrowing periods may be quite long, but subject to recalls upon the request of another patron, effectively shortening the loan period.

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Also:

The re-registration of a borrower at the end of the established period of library membership. This may be done to keep patrons' addresses and contact information up-to-date.

To extend the period during which a periodical subscription will be delivered, usually by an additional year or period of years, in exchange for payment of a fixed fee by the subscriber.