In the morning, accustomed to being diverted (6)
I believe the answer is:
amused
'being diverted' is the definition.
('amused' can be a synonym of 'diverted')
'in the morning accustomed' is the wordplay.
'in the morning' becomes 'am' (AM on a clock).
'accustomed' becomes 'used' (I've seen this in other clues).
'am'+'used'='AMUSED'
'to' is the link.
(Other definitions for amused that I've seen before include "Made (someone) laugh" , "Tickled pink" , "Mildly diverted or entertained" , "Beguiled" , "Mildly entertained by Medusa" .)