Bishop getting on with one in residence, showing great friendliness (8)
I believe the answer is:
bonhomie
'great friendliness' is the definition.
(bonhomie is friendliness)
'bishop getting on with one in' is the wordplay.
'bishop' becomes 'B' (abbreviation for bishop in chess).
'getting' means one lot of letters go next to another.
'with' is an insertion indicator.
'one' becomes 'i' (Roman numeral).
'in' becomes 'home' ('he's in' can mean 'he's home').
'i' inserted into 'home' is 'homie'.
'b'+'on'+'homie'='BONHOMIE'
'residence showing' acts as a link.
I am not very happy about this link. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for bonhomie that I've seen before include "Inventory" , "'Affability, geniality (8)'" , "Genial manner from hobo in me" , "Exuberant friendliness - goodwill" , "Good fellowship or genial manner in France" .)