Sleepy day arguments ultimately carry (6)
I believe the answer is:
drowsy
'sleepy' is the definition.
(I've seen this before)
'day arguments ultimately carry' is the wordplay.
'day' becomes 'd' (abbreviation for day).
'arguments' becomes 'rows' (I've seen this in another clue).
'ultimately' indicates one should take the final letters.
The last letter of 'carry' is 'y'.
'd'+'rows'+'y'='DROWSY'
(Other definitions for drowsy that I've seen before include "Being rather tired" , "Disinclined to stay awake" , "Nodding off" , "Soporific" , "Dull" .)