Occupy or employ for half a day (5)
I believe the answer is:
amuse
'occupy' is the definition.
(thesaurus)
'half a day' is the wordplay.
'half' means to take half the letters.
'a' becomes 'an'.
'day' becomes 'muse' (I can't explain this - if you can you should believe this answer much more).
'an' cut in half is 'a'.
'a'+'muse'='AMUSE'
'or employ for' is the link.
This may not be correct. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for amuse that I've seen before include "Keep occupied" , "Cause to laugh or smile" , "Tickle" , "Delight" , "Pleasantly occupy" .)