Monarch's authority goes for good during pinkish regime (8)
I believe the answer is:
kingship
'pinkish regime' is the definition.
Although both the answer and definition are singular nouns, I can't see how they can define each other.
'monarch's authority goes for good during' is the wordplay.
'monarch' becomes 'K' (abbreviation for king in chess).
'authority goes' becomes 'inship' (I can't explain this - if you can you should believe this answer much more).
'for' means one lot of letters go next to another.
'good' becomes 'g' (abbreviation).
'during' is an insertion indicator.
'k'+'inship'='kinship'
'kinship' going around 'g' is 'KINGSHIP'.
Can you help me to learn more?
(Other definitions for kingship that I've seen before include "Sovereignty" , "palace office" , "Monarch's status" , "Sovereign's office" , "Royalty" .)