Looking embarrassed, being wrong about hard misleading clue (3,7)
I believe the answer is:
red herring
'misleading clue' is the definition.
(I've seen this before)
'looking embarrassed being wrong about hard' is the wordplay.
'looking embarrassed' becomes 'red' (I've seen this before).
'being wrong' becomes 'erring' (I've seen this before).
'about' says to put letters next to each other.
'hard' becomes 'h' (abbreviation used in pencil classifications).
'erring' put after 'h' is 'herring'.
'red'+'herring'='RED HERRING'
(Other definitions for red herring that I've seen before include "Misleading clue" , "Irrelevant topic" , "bait, of a certain sort" , "What distracts" , "Diversion intended to distract attention from the main issue" .)