Second tirade about department is caustic (7)
I believe the answer is:
mordant
'is caustic' is the definition.
(I've seen this before)
'second tirade about department' is the wordplay.
'second' becomes 'mo' (both are short periods of time).
'tirade' becomes 'rant' (both can mean an angry outburst).
'about' is an insertion indicator.
'department' becomes 'd' (abbreviation eg in MOD Ministry of Defence).
'rant' going around 'd' is 'rdant'.
'mo'+'rdant'='MORDANT'
(Other definitions for mordant that I've seen before include "Corrosive" , "Biting, scathing" , "Acerbic" , "Acrimonious" , "Bitingly sarcastic" .)