Socialist loves to run in, determined (8)
I believe the answer is:
resolved
'determined' is the definition.
(resolving is a kind of determining)
'socialist loves to run in' is the wordplay.
'socialist' becomes 'red' (red can informally mean a socialist).
'to run' indicates anagramming the letters.
'in' means one lot of letters goes inside another.
'loves' with letters rearranged gives 'solve'.
'red' enclosing 'solve' is 'RESOLVED'.
(Other definitions for resolved that I've seen before include "Not put off" , "Settled, found a solution" , "Settled; determined" , "Settled a dispute" , "Firmly determined" .)