Show embarrassment, ultimately going pink (4)
I believe the answer is:
gore
'pink' is the definition.
(thesaurus)
I cannot understand how the rest of the clue works.
Can you help me to learn more?
(Other definitions for gore that I've seen before include "stuff from part of Kensington" , "Pierce or wound with a horn or tusk" , "Showing guts" , "piece of material" , "Bloodshed" .)