Fish gobbling fellow up in coat (6)
I believe the answer is:
enamel
'coat' is the definition.
(enamel is a kind of coat)
'fish gobbling fellow up' is the wordplay.
'fish' becomes 'eel' (eel is a type of fish).
'gobbling' indicates putting letters inside.
'fellow' becomes 'man' (fellow can mean a man).
'up' says the letters should be written backwards (in down clue: letters go upwards).
'man' back-to-front is 'nam'.
'eel' going around 'nam' is 'ENAMEL'.
'in' acts as a link.
(Other definitions for enamel that I've seen before include "Glassy substance" , "Hard shiny coating on surface" , "Crown Protector?" , "Nail polish" , "Outer tooth material" .)