Off-cream on the outside, the inside in red (7)
I believe the answer is:
carmine
'red' is the definition.
(carmine is a kind of red)
'off-cream on the outside the inside' is the wordplay.
'off' indicates anagramming the letters.
'on the outside' indicates putting letters inside.
'the inside' becomes 'in'.
'cream' is an anagram of 'carme'.
'carme' going around 'in' is 'CARMINE'.
'in' is the link.
(Other definitions for carmine that I've seen before include "Vivid red colour" , "Crimson pigment" , "Bright red" .)