"A false premise," I'd put in, "when it comes to skin" (9)
I believe the answer is:
epidermis
'skin' is the definition.
(I've seen this before)
'a false premise i'd put in' is the wordplay.
'a false' indicates anagramming the letters.
'put in' means one lot of letters goes inside another.
'premise' anagrammed gives 'epermis'.
'epermis' enclosing 'id' is 'EPIDERMIS'.
'when it comes to' is the 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 epidermis that I've seen before include "Outermost layer" , "Protective covering" , "Outer layer of skin" , "Surface of the skin" .)