Shred half of the letters (4)
I believe the answer is:
atom
'shred' is the definition.
(both can mean a tiny amount of something)
'half of the letters' is the wordplay.
I cannot quite understand how this works, but
'of' could be 'o' and 'o' is found within the answer.
'the' could be 't' (the is pronounced as a 't' sound in some dialects) and 't' is present in the answer.
The remaining letters 'am' is a valid word which might be clued in a way I don't understand.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for atom that I've seen before include "Moat (anag.)" , "Scrap" , "Tiny particle, great bomb" , "little amount" , "Piece of matter in moat" .)