Having a go at tiresome job for judge (6)
I believe the answer is:
trying
This clue is a triple definition!
'having a go' is the first definition.
(having a go at something is trying it)
'at' is a link.
'tiresome' is the second definition.
(trying can mean annoying or tiresome)
'job for judge' is the third definition.
(a judge tries defendants)
(Other definitions for trying that I've seen before include "Making attempts" , "Essaying" , "Causing strain, annoying" , "activity in court?" , "Testing" .)