Great friendliness of bishop on one being invited into dwelling (8)
I believe the answer is:
bonhomie
'great friendliness' is the definition.
(bonhomie is friendliness)
'bishop on one being invited into dwelling' is the wordplay.
'bishop' becomes 'B' (chess abbreviation).
'one' becomes 'I' (Roman numeral).
'being invited into' is an insertion indicator.
'dwelling' becomes 'home' (synonyms).
'i' going inside 'home' is 'homie'.
'b'+'on'+'homie'='BONHOMIE'
'of' is the link.
(Other definitions for bonhomie that I've seen before include "'Easy good nature, cheerful friendliness (8)'" , "Inventory" , "Exuberant friendliness - goodwill" , "Good-natured friendliness" , "'Affability, geniality (8)'" .)