Fabric seen around the centre of mats (6)
I believe the answer is:
sateen
'fabric' is the definition.
(I know that sateen is a type of fabric)
'seen around the centre of mats' is the wordplay.
'around' means one lot of letters goes inside another.
'the centre of' means to look at the middle letters.
The middle letters of 'mats' are 'at'.
'seen' going around 'at' is 'SATEEN'.
(Other definitions for sateen that I've seen before include "Sea net could provide a glossy fabric" , "Glossy cotton fabric" , "Cotton fabric with a shiny finish" , "Shiny cloth found in senate" , "Glossy material" .)