Bishop and religious fraternity row about stray dog (6,7)
I believe the answer is:
border terrier
'stray dog' is the definition.
'Border terrier' can be an answer for 'dog' (Border terrier is an example). I am unsure of the 'stray' bit.
'bishop and religious fraternity row' is the wordplay.
'bishop' becomes 'B' (abbreviation for bishop in chess).
'and' means one lot of letters go next to another.
'religious fraternity' becomes 'order' (I've seen this before).
'row' becomes 'terrier' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'b'+'order'+'terrier'='BORDER TERRIER'
'about' acts as a link.
Can you help me to learn more?
(Other definitions for border terrier that I've seen before include "who might have engaged in action near the Tweed?" , "Rough-haired dog" .)