No time for fear? That's a mistake! (5)
I believe the answer is:
error
'a mistake' is the definition.
('error' can be a synonym of 'mistake')
'no time for fear?' is the wordplay.
'no' is a deletion indicator.
'time for' becomes 't' (I've seen this in other clues).
'fear?' becomes 'terror' (terror is a kind of fear).
'terror' with 't' taken out is 'ERROR'.
'that's' acts as a link.
(Other definitions for error that I've seen before include "wrong" , "1 down" , "Trial and ___" , "Mistake from terrorist" , "A mistake or inaccuracy" .)