Engages the man, surrounded by chaos (6)
I believe the answer is:
meshes
'engages' is the definition.
('mesh' can be a synonym of 'engage')
'the man surrounded by chaos' is the wordplay.
'the man' becomes 'he'.
'surrounded by' means one lot of letters goes inside another.
'chaos' becomes 'mess' (I've seen this before).
'he' placed into 'mess' is 'MESHES'.
(Other definitions for meshes that I've seen before include "Engages with others - using nets?" , "gets engaged" , "Becomes entangled or fits together" , "Co-ordinates" , "Fits into, intertwines" .)