Shy about being popular, but bright (5)
I believe the answer is:
shiny
'bright' is the definition.
(I've seen this before)
'shy about being popular' is the wordplay.
'about' is an insertion indicator.
'being popular' becomes 'in'.
'shy' placed around 'in' is 'SHINY'.
'but' acts as a link.
(Other definitions for shiny that I've seen before include "Polished, reflective" , "Smooth and polished" , "Smooth and reflective" , "Bright" , "Lustrous, glossy" .)