In the morning one day... (4)
I believe the answer is:
amid
'in' is the definition.
'morning one day' is the wordplay.
'morning' becomes 'am' (as in 12:00 AM).
'one' becomes 'i' (Roman numeral).
'day' becomes 'd' (abbreviation for day).
'am'+'i'+'d'='AMID'
'the' acts as a link.
(Other definitions for amid that I've seen before include "A dim sort of preposition" , "In the middle of" , "Within" , "Surrounded by" , "In the thick of" .)