Prima donna is overly keen (4)
I believe the answer is:
avid
'keen' is the definition.
(both can mean enthusiastic)
I cannot understand how the rest of the clue works.
Can you help me to learn more?
(Other definitions for avid that I've seen before include "Extremely enthusiastic" , "Fervent" , "Greedy like diva" , "Greedy or eagerly desirous" , "In operation" .)