Called Edward out one morning (5)
I believe the answer is:
named
'called' is the definition.
('name' can be a synonym of 'call')
'edward out one morning' is the wordplay.
'edward' becomes 'ned' ().
'out' indicates putting letters inside.
'one morning' becomes 'am' (as in ne:00 AM).
'ned' placed around 'am' is 'NAMED'.
(Other definitions for named that I've seen before include "Identified by appellation" , "Handled" , "Entitled" , "Titled" , "Designated" .)