Award given to player on screen, opener doffing cap (4)
I believe the answer is:
emmy
'award' is the definition.
(I know that Emmy is a type of award)
I cannot understand how the remainder of the clue works.
Can you help me to learn more?
(Other definitions for emmy that I've seen before include "British television award" , "Academy of Television Arts and Sciences award" , "Least complicated" , "American television award" , "US TV award" .)