Obsession about no. 1 mug colour (10)
I believe the answer is:
complexion
'mug colour' is the definition.
'complexion' can be an answer for 'colour' (complexion is a kind of colour). I'm not sure about the 'mug' bit.
'obsession about no 1' is the wordplay.
'obsession' becomes 'complex' (I can't justify this - if you can you should give a lot more credence to this answer).
'about' shows that the letters should be reversed in order.
'no c' becomes 'no i' (resembles No c).
'noi' written backwards gives 'ion'.
'complex'+'ion'='COMPLEXION'
Can you help me to learn more?
(Other definitions for complexion that I've seen before include "Look" , "character" , "Skin tone" , "Face" , "Nature" .)