Somewhat dishonest, shy about publicity (5)
I believe the answer is:
shady
'somewhat dishonest' is the definition.
'shady' can be an answer for 'dishonest' (I've seen this before). I'm unsure of the 'somewhat' bit.
'shy about publicity' is the wordplay.
'about' indicates putting letters inside.
'publicity' becomes 'ad' (short for advert).
'shy' going around 'ad' is 'SHADY'.
Can you help me to learn more?
(Other definitions for shady that I've seen before include "Of questionable morality out of the sunlight" , "Disreputable -- out of the sun" , "Suspicious, fishy" , "Of doubtful legality" , "Dubious (of character)" .)