It's a rigid rule (9)
I believe the answer is:
yardstick
'rule' is the definition.
(I know that Yardstick is a type of rule)
I cannot understand how the rest of the clue works.
Can you help me to learn more?
(Other definitions for yardstick that I've seen before include "Guideline" , "Benchmark" , "measure of performance" , "Measuring rod" , "Measure against which to make comparison" .)