Bussing company nearly employing one from another branch that’s close (7,6)
I believe the answer is:
kissing cousin
'one from another branch that's close' is the definition.
(term for a cousin one is close to)
'bussing company nearly employing' is the wordplay.
'bussing' becomes 'kissing' ('kiss' can be a synonym of 'buss').
'company' becomes 'co' (abbreviation).
'nearly' means to remove the last letter.
'employing' becomes 'using' ('use' can be a synonym of 'employ').
'using' with its final letter taken away is 'usin'.
'kissing'+'co'+'usin'='KISSING COUSIN'
(Other definitions for kissing cousin that I've seen before include "More or less distant relative" , "Distant but familiar relative" , "Intimate relative" .)