Panic, losing head? That’s a mistake (5)
I believe the answer is:
error
'a mistake' is the definition.
('error' can be a synonym of 'mistake')
'panic losing head?' is the wordplay.
'panic' becomes 'terror' (synonyms).
'losing head?' means to remove the first letter.
'terror' with its first letter taken off is 'ERROR'.
'that's' acts as a link.
(Other definitions for error that I've seen before include "Mistake from terrorist" , "Faulty judgment" , "Slip, mistake" , "Miscarriage of justice" , "Fallacy, mistake" .)