Have confidence over investigator (female) — never good to show disloyalty (8)
I believe the answer is:
betrayal
'disloyalty' is the definition.
(I know that betrayal is a type of subversiveness)
I don't understand how the remainder of the clue works.
(Other definitions for betrayal that I've seen before include "Treacherous divulgence" , "sale" , "Treacherous act" , "letting side down" , "Breaking of trust" .)