They produce straight lines of monarchs (6)
'monarchs' is the definition.
(I've seen this before)
I don't understand how the rest of the clue works.
Can you help me to learn more?
(Other definitions for rulers that I've seen before include "they must not be crooked", "Measuring sticks", "Strips with straight edge to measure", "Drawing sticks or monarchs", "Sticks marked off in units".)