In private, a serious and particularly baffling problem (6)
I believe the answer is:
teaser
'particularly baffling problem' is the definition.
'teaser' can be an answer for 'problem' (I've seen this before). I'm not certain of the 'particularly baffling' bit.
'in private a serious' is the wordplay.
'in' indicates the answer is hidden within the clue.
'TEASER' can be found hidden inside 'private a serious'.
'and' acts as a link.
Can you help me to learn more?
(Other definitions for teaser that I've seen before include "One who irritates playfully" , "Tricky question; intriguing ad" , "one using a backcomb" , "Difficult question" , "Tricky question; intriguing preliminary advert" .)