Squeal about lecture that's haunting (8)
I believe the answer is:
stalking
'haunting' is the definition.
('stalk' can be a synonym of 'haunt')
'squeal about lecture' is the wordplay.
'squeal' becomes 'sing' (both can mean to act as an informant).
'about' indicates putting letters inside.
'lecture' becomes 'talk' (synonyms).
'sing' going around 'talk' is 'STALKING'.
'that's' acts as a link.
(Other definitions for stalking that I've seen before include "Carefully following" , "After game" , "Covertly following" , "Following stealthily" , "providing unwanted attention?" .)