Tilt one square, checking finishing touches of cyclic quadrilateral (7)
I believe the answer is:
incline
'tilt' is the definition.
(inclining is a kind of tilting)
I don't understand the rest of the clue.
Can you help me to learn more?
(Other definitions for incline that I've seen before include "Tend - slope" , "Be disposed to" , "Lean (towards)" , "Turn" , "Bend forwards" .)