Provided turning circles on courtyard and detail of their execution (6,5)
I believe the answer is:
firing squad
'detail of their execution' is the definition.
I can't judge whether this definition defines the answer.
'provided turning circles on courtyard' is the wordplay.
'provided' becomes 'if' (eg 'provided it's sunny' means 'if it's sunny').
'turning' is a reversal indicator.
'circles' becomes 'rings' ('ring' can be a synonym of 'circle').
'on' means one lot of letters go next to another (in a down clue, letters appear on others).
'courtyard' becomes 'quad' (short for quadrangle).
'if' back-to-front is 'fi'.
'fi'+'rings'+'quad'='FIRING SQUAD'
'and' is the link.
Can you help me to learn more?
(Other definitions for firing squad that I've seen before include "Line of executioners" , "Group detailed to shoot condemned prisoner" , "Military group carrying out death sentence" , "Shooting party" , "Military executioners" .)