Panic doesn’t start by mistake (5)
I believe the answer is:
error
'mistake' is the definition.
(I know that mistake can be written as error)
'panic doesn't start' is the wordplay.
'panic' becomes 'terror' (synonyms).
'doesn't start' means to remove the first letter.
'terror' with its first letter removed is 'ERROR'.
'by' acts as a link.
(Other definitions for error that I've seen before include "Mistake, lapse" , "Faulty judgment" , "Trial and ___" , "wrongdoing" , "Miscalculation" .)