Turned over rugs in academy showing endurance (7)
I believe the answer is:
stamina
'endurance' is the definition.
(I know that stamina is a type of endurance)
'turned over rugs in academy' is the wordplay.
'turned over' is a reversal indicator.
'rugs' becomes 'mats' (I've seen this before).
'academy' becomes 'a' (abbreviation for academy).
'mats' in reverse letter order is 'stam'.
'stam'+'in'+'a'='STAMINA'
'showing' acts as a link.
(Other definitions for stamina that I've seen before include "The ability to sustain prolonged physical or mental effort" , "Energy and staying power" , "Endurance, strength to stay the course" , "capability to keep going" , "Staying power, ability to withstand prolonged strain" .)