Dark-complexioned, but self-conscious about a wart (7)
I believe the answer is:
swarthy
'dark-complexioned' is the definition.
(I've seen this before)
'self-conscious about a wart' is the wordplay.
'self-conscious' becomes 'shy' (I've seen this in another clue).
'about' is an insertion indicator.
'shy' placed around 'wart' is 'SWARTHY'.
'but' acts as a link.
(Other definitions for swarthy that I've seen before include "Having a dark complexion" , "Dark-skinned" , "Dark complexioned" , "Dark-complexioned" , "Dark skin" .)