Misleading clue embarrassed Hercule, initially making a mistake (3,7)
I believe the answer is:
red herring
'misleading clue' is the definition.
(I've seen this before)
'embarrassed hercule initially making a mistake' is the wordplay.
'embarrassed' becomes 'red' (I've seen this before).
'initially' indicates taking the first letters.
'making a mistake' becomes 'erring' ('err' can be a synonym of 'make a mistake').
The first letter of 'hercule' is 'h'.
'red'+'h'+'erring'='RED HERRING'
(Other definitions for red herring that I've seen before include "food?" , "An irrelevance" , "Cover" , "fish" , "What distracts" .)