Public demonstration possibly skipping first bridge (4)

I believe the answer is:
arch
'bridge' is the definition.
(I've seen this before)
I cannot understand how the remainder of the clue works.
Can you help me to learn more?
(Other definitions for arch that I've seen before include "Leading figures" , "Shrewd; bridge" , "Chief; bow" , "Knowing, coy" , "Construction with a keystone" .)
