Went round with the man sweetheart escorted (7)
I believe the answer is:
wheeled
'went round' is the definition.
'with the man sweetheart escorted' is the wordplay.
'with' becomes 'w' (abbreviation**).
'the man' becomes 'he'.
'sweetheart' becomes 'e' (the heart/centre of 'sweet').
'escorted' becomes 'led'.
'w'+'he'+'e'+'led'='WHEELED'
(Other definitions for wheeled that I've seen before include "'Revolved, circled (7)'" , "Roamed" , "Turned in a wide circle" .)