Proceed controversially welcoming monarch and Republican hierarchy (7,5)
I believe the answer is:
pecking order
'hierarchy' is the definition.
(synonyms)
'proceed controversially welcoming monarch and republican' is the wordplay.
I cannot really see how this works, but
'proceed' could be 'go' (synonyms) and 'go' is found within the answer.
'monarch' could be 'er' (abbreviation for Elizabeth Regina, British Queen) and 'er' is found in the answer.
'and' could be 'n' (common abbreviation for 'and') and 'n' is found in the answer.
'republican' could be 'r' (abbreviation) and 'r' is present in the answer.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for pecking order that I've seen before include "Gradation" , "Animal Farm hierarchy" , "Hierarchy (of hens?)" .)