In Paris, and after training, one's invaluable in the kitchen (7)
I believe the answer is:
skillet
'one's invaluable in the kitchen' is the definition.
(type of cooking pan or pot)
'in paris and after training' is the wordplay.
'in paris and' becomes 'et' ('and' in French).
'after' means one lot of letters go next to another.
'training' becomes 'skill' (someone with a skill has undergone training).
'et' put after 'skill' is 'SKILLET'.
(Other definitions for skillet that I've seen before include "Small cooking pot" , "Frying-pan" , "Metal cooking pot with long handle" , "Cooking-pot" , "Long-handled cooking pot" .)