Leave everything out there, competing eagerly (5)
I believe the answer is:
vying
'competing eagerly' is the definition.
'vying' can be an answer for 'competing' ('vie' can be a synonym of 'compete'). I am unsure of the 'eagerly' bit.
I don't understand the rest of the clue.
Can you help me to learn more?
(Other definitions for vying that I've seen before include "Striving" , "Struggling" , "Competing (with others)" , "Eagerly competing" , "in contention" .)