A milder form of hell will, we hear, disrupt routine (6)
I believe the answer is:
heckle
'disrupt routine' is the definition.
(as in disrupting a comedian's routine)
'a milder form of hell will we hear' is the wordplay.
'a milder form of hell' becomes 'heck' (euphemism for hell).
'will' becomes ''ll' (contracted form, as in 'he'll' - 'he will').
'we hear' indicates a 'sounds like' (homophone) clue.
'll' sounds like 'le'.
'heck'+'le'='HECKLE'
(Other definitions for heckle that I've seen before include "bait?" , "Noisily interrupt (a speaker)" , "Shout from the audience" , "Interrupt (a public speaker) with taunts" , "Harass a speaker" .)