After covering the bottom half, rubs body (4)
I believe the answer is:
mass
'half rubs body' is the definition.
'mass' can be an answer for 'body' (mass is a kind of body). I am unsure of the 'half rubs' bit.
'after covering the bottom' is the wordplay.
'after covering' becomes 'm' (I can't explain this - if you can you should give a lot more credence to this answer).
'the bottom' becomes 'ass' ('ass' can be a synonym of 'bottom').
'm'+'ass'='MASS'
Can you help me to learn more?
(Other definitions for mass that I've seen before include "Total" , "Body of matter" , "Church rite; large group" , "Religious celebration" , "Lump of material" .)