Upholstery
Upholstery (noun) /ʌpˈhəʊl.stər.i/ US /-ˈhoʊl.stɚ-/
a piece of cloth or fabric used to cover furniture – work of upholstery – fabric – covers – material – stuffing – veneer- coating:
The sofa was rather old. So, we covered it with some upholstery.