If slimming, you can’t live on half of it! (4)
I believe the answer is:
diet
'if slimming you can't' is the definition.
I can't judge whether this definition defines the answer.
'live on half of it' is the wordplay.
'live' becomes 'die' (I am not sure about this - if you are sure you should believe this answer much more).
'on' is a charade indicator (letters next to each other).
'half of' suggests halving the letters.
'it' with half the letters taken is 't'.
'die'+'t'='DIET'
Can you help me to learn more?
(Other definitions for diet that I've seen before include "Restricted cheer" , "Special food regime" , "Fast - food - convention" , "Legislative assembly; food regimen" , "Restriction of food intake" .)