Paint coat of eggshell around handle (6)
I believe the answer is:
enamel
'paint' is the definition.
(I've seen this before)
'coat of eggshell around handle' is the wordplay.
'coat of' says to hollow out the word (remove centre letters).
'around' means one lot of letters goes inside another.
'handle' becomes 'name' (I've seen this before).
'eggshell' with its middle removed is 'el'.
'el' placed around 'name' is 'ENAMEL'.
(Other definitions for enamel that I've seen before include "protective coat" , "found on crowns" , "Hard white substance covering the crown of a tooth" , "hard cover" , "Outer tooth material" .)