undersleeve

un·der·sleeve

 (ŭn′dər-slēv′)
n.
1. A sleeve worn under another.
2. An ornamental sleeve worn under another sleeve, designed to extend below or show through slashes in the outer sleeve.
American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2016 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

undersleeve

(ˈʌndəˌsliːv)
n
(Clothing & Fashion) the lower of two sleeves
Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014