the part of a garment that covers the arm, varying in form and length but commonly tubular.

an envelope, usually of paper, for protecting a phonograph record.

Machinery . a tubular piece, as of metal, fitting over a rod or the like.

to furnish with sleeves.

Machinery . to fit with a sleeve; join or fasten by means of a sleeve. ?

have something up one's sleeve, to have a secret plan, scheme, opinion

or the like

I could tell by her sly look that she had something up her sleeve.

laugh up or in one's sleeve

to be secretly amused or contemptuous; laugh inwardly

to laugh up one's sleeve at someone's affectations.