Tedious job that's essential, husband interrupts (5)
I believe the answer is:
chore
'tedious job' is the definition.
(I've seen this in another clue)
'essential husband interrupts' is the wordplay.
'essential' becomes 'core' (both can mean very important).
'husband' becomes 'h' (abbreviation).
'interrupts' is an insertion indicator.
'core' placed around 'h' is 'CHORE'.
'that's' is the link.
(Other definitions for chore that I've seen before include "Manipulate; name" , "Boring task" , "Mundane task" , "easy option? Not so!" , "Unpleasant task" .)