outsert
/ˈaʊtsər, ˈaʊt-sɜr/Definitions
1. noun
A sleeve or cover that fits over the outer cover of a book or other item
“The outsert of the hardcover book was damaged in transit.”
2. verb
To attach or insert an outsert into a book or other item
“The bookseller outserted the new hardcover cover onto the book.”