Show rug I want shortened (7)
I believe the answer is:
matinee
'show' is the definition.
(matinee is a kind of show)
'rug i want shortened' is the wordplay.
'rug' becomes 'mat' (both are floor coverings).
'want' becomes 'need' (needing is a kind of wanting).
'shortened' means to remove the last letter.
'need' with its final letter removed is 'nee'.
'mat'+'i'+'nee'='MATINEE'
(Other definitions for matinee that I've seen before include "Afternoon showing of play" , "After lunch, show" , "Afternoon show" , "First jackets" , "Performance held in the afternoon" .)