Start removing odd characters? Brilliant suggestion! (5)
I believe the answer is:
trace
'suggestion' is the definition.
(I've seen this before)
'start removing odd characters? brilliant' is the wordplay.
'removing odd characters?' means one should take alternating letters.
'brilliant' becomes 'ace' (I've seen this before).
The alternating letters of 'start' are 'tr'.
'tr'+'ace'='TRACE'
(Other definitions for trace that I've seen before include "Hunt down" , "indicator" , "Barely detectable amount" , "Vestige; manage to find" , "a piece of harness" .)