Small object does not have small volume (4)
I believe the answer is:
peck
'volume' is the definition.
(thesaurus)
'small object' is the wordplay.
'small' becomes 'pec' (I can't explain this - if you can you should believe this answer much more).
'object' becomes 'K' (K is an example).
'pec'+'k'='PECK'
'does not have small' acts as a 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 peck that I've seen before include "Bite lightly; a dry measure" , "lot of pints" , "Perfunctory kiss" , "Gregory" , "Large number" .)