Host runs last equal (7)
I believe the answer is:
compeer
This might be a double definition.
'host runs last' is the first definition.
The answer and definition can be both people as well as being singular nouns.
Maybe there's a link between them I don't understand?
'equal' is the second definition.
('compeer' can be a synonym of 'equal')
(Other definitions for compeer that I've seen before include "being of equal status" , "Fellow" , "social match?" .)