sleeve
US /sliːv/
UK /sliːv/

1.
the part of a garment that covers the arm
:
•
He rolled up his sleeves and got to work.
•
The dress has long sleeves.
2.
a protective covering for something, typically cylindrical or open at both ends
:
•
He put the record back in its cardboard sleeve.
•
The coffee cup came with a protective sleeve.