Bashful, possibly embarrassed star (3,5)
I believe the answer is:
red dwarf
'bashful possibly embarrassed star' is the definition.
'red dwarf' can be an answer for 'star' (red dwarf is a kind of star). I am not certain of the 'bashful possibly embarrassed' bit.
'embarrassed star' is the wordplay.
'embarrassed' becomes 'red' (someone may blush or go red when embarrassed).
'star' becomes 'dwarf' (I can't justify this - if you can you should believe this answer much more).
'red'+'dwarf'='RED DWARF'
Can you help me to learn more?
(Other definitions for red dwarf that I've seen before include "Old cool star" , "Small, cool star - TV show" , "Small old cooling star" .)