Assumption that a place of business is unfinished (7)
I believe the answer is:
premise
'assumption' is the definition.
('premise' can be a synonym of 'assumption')
'a place of business is unfinished' is the wordplay.
'a place of business' becomes 'premises' (I've seen this before).
'is unfinished' means to remove the last letter.
'premises' with its final letter taken off is 'PREMISE'.
'that' is the link.
(Other definitions for premise that I've seen before include "Basis of theory" , "It's presumed" , "argument" , "Statement that is assumed to be true and from which a conclusion can be drawn" , "Statement on which reasoning is based" .)