Lost a day finishing work! (4)
I believe the answer is:
sunk
'lost' is the definition.
(lost at sea)
'a day finishing work' is the wordplay.
'a day' becomes 'sun' (abbreviation for Sunday).
'finishing' suggests the final letters (the letter which finishes the word).
The final letter of 'work' is 'k'.
'sun'+'k'='SUNK'
(Other definitions for sunk that I've seen before include "ruined" , "Submerged" , "Doomed - bored" , "suffered decline" , "Dropped; in a fix" .)