Keen for a piece of the action at the end of June (5)
I believe the answer is:
acute
'keen' is the definition.
(I know that keen can be written as acute)
'a piece of the action at the end of june' is the wordplay.
'piece of the action' becomes 'cut' (I've seen this in another clue).
'at the end of' says to take the final letters.
The last letter of 'june' is 'e'.
'a'+'cut'+'e'='ACUTE'
'for' is the link.
(Other definitions for acute that I've seen before include "Excruciating" , "Sharp like angle" , "Severe, penetrating" , "Shrewd; severe" , "(Of an angle) less than 90deg" .)