Work for the county and get demoted (2,4)
I believe the answer is:
go down
'get demoted' is the definition.
I can't tell whether this definition defines the answer.
'work for the county' is the wordplay.
'work' becomes 'go' (synonyms).
'for' means one lot of letters go next to another.
'the county' becomes 'down' (county of Northern Ireland).
'go'+'down'='GO-DOWN'
'and' acts as a link.
Can you help me to learn more?
(Other definitions for go down that I've seen before include "leave university" , "Be recorded" , "Drop" , "Warehouse" , "Sink" .)