Always following Republican rite about dog (9)
I believe the answer is:
retriever
'dog' is the definition.
(eg a Golden Retriever)
'always following republican rite about' is the wordplay.
'always' becomes 'ever' (synonyms).
'following' says to put letters next to each other.
'republican' becomes 'r' (abbreviation).
'about' is an anagram indicator.
'rite' is an anagram of 'etri'.
'r'+'etri'='retri'
'ever' put after 'retri' is 'RETRIEVER'.
(Other definitions for retriever that I've seen before include "He rescues" , "Pet" , "Breed of dog" , "Gun-dog, may be golden" , "Dog bred to fetch game" .)