Performed with a cold jerk that’s preachy (8)
I believe the answer is:
didactic
'preachy' is the definition.
(I've seen this in another clue)
'performed with a cold jerk' is the wordplay.
'performed' becomes 'did' ('do' can be a synonym of 'perform').
'with' is a charade indicator (letters next to each other).
'cold' becomes 'C' (eg on taps).
'jerk' becomes 'tic' (jerking movement by the body).
'did'+'a'+'c'+'tic'='DIDACTIC'
'that's' is the link.
(Other definitions for didactic that I've seen before include "Having the manner of one lecturing pupils" , "Intended to teach or instruct" , "'Instructive, perhaps excessively so (8)'" , "like a school-teacher?" , "Having the manner of one lecturing students" .)