Type of bridge: brilliant crossing over from the other side (10)
I believe the answer is:
cantilever
'type of bridge' is the definition.
(I've seen this in another clue)
'brilliant crossing over from the other side' is the wordplay.
'brilliant' becomes 'clever' (I've seen this before).
'crossing' means one lot of letters goes inside another.
'over from the other side' becomes 'anti' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'clever' placed around 'anti' is 'CANTILEVER'.
Can you help me to learn more?
(Other definitions for cantilever that I've seen before include "Projecting beam fixed at one end" , "support at one end" , "Beam supported at only one end" , "bridge design" , "Projecting mass" .)