Floor coverings rolled back in area displaying grit (7)
I believe the answer is:
stamina
'grit' is the definition.
(thesaurus)
'floor coverings rolled back in area' is the wordplay.
'floor coverings' becomes 'mats' (mat is a kind of floor covering).
'rolled back' says the letters should be written backwards.
'area' becomes 'a' (maths abbreviation).
'mats' back-to-front is 'stam'.
'stam'+'in'+'a'='STAMINA'
'displaying' acts as a link.
(Other definitions for stamina that I've seen before include "energy to go on" , "The ability to sustain prolonged physical or mental effort" , "capability to keep going" , "grit" , "Ability for sustained effort" .)