Almost the last round house (4)
I believe the answer is:
semi
This clue is a double definition.
'almost the last round' is the first definition.
(round before final in sports contests)
'house' is the second definition.
(I've seen this before)
(Other definitions for semi that I've seen before include "Common type of house" , "Not detached house" , "Prefix meaning half (4)" , "Property attached to another" , "Half (pfx)" .)