Embarrassed sleuth breaks into exasperated expression (8)
I believe the answer is:
sheepish
'embarrassed' is the definition.
(I've seen this before)
'sleuth breaks into exasperated expression' is the wordplay.
'sleuth' becomes 'pi' (private investigator).
'breaks into' is an insertion indicator (inserted letters break into the word).
'exasperated expression' becomes 'sheesh' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'pi' placed within 'sheesh' is 'SHEEPISH'.
Can you help me to learn more?
(Other definitions for sheepish that I've seen before include "Bashful and embarrassed like woolly creature" , "Embarrassed in woolly way?" , "Embarrassed through shame; ovine" , "embarrassment" , "describing 3 [ROMNEY] ?" .)