Went off in that direction (4)
I believe the answer is:
left
This clue might be a double definition.
'went off in that' is the first definition.
'left' can be an answer for 'went' (as in leaving). I'm not certain of the remainder of the definition.
'direction' is the second definition.
(I have seen 'Socialist direction' mean 'left' so perhaps 'direction' could also mean 'left')
Can you help me to learn more?
(Other definitions for left that I've seen before include "political grouping" , "not consumed" , "Socialist direction" , "Possibly radical" , "Vacated; political wing" .)