Get to cover short business-like lecture (8)
I believe the answer is:
Here is my best explanation:
'lecture' is the definition.
'get to cover short business' is the subsidiary indication.
'get to' becomes 'reach' ('reach' can be a synonym of 'get to').
'cover' is an insertion indicator.
'short business' becomes 'pro' (I can't explain this - if you can you should give a lot more credence to this answer).
'reach' enclosing 'pro' is 'reproach'.
'like' is the link.
(Other definitions for reproach that I've seen before include "Upbraid, rebuke", "Admonition", "Scold(ing)", "Castigate", "Reprove gently", "Gently reprove", "Expression of disapproval", "Rebuke or expression of disappointment", "Take to task" and "Express disapproval to (someone)".)