Dread losing face making a mistake (5)
I believe the answer is:
error
'a mistake' is the definition.
('error' can be a synonym of 'mistake')
'dread losing face' is the wordplay.
'dread' becomes 'terror' (I've seen this before).
'losing face' means to remove the first letter.
'terror' with its initial letter removed is 'ERROR'.
'making' is the link.
(Other definitions for error that I've seen before include "Mistake or mishap" , "Blunder, slip" , "Slip, mistake" , "Gaffe" , "Boo-boo" .)