Green space -- excited ape seen within repeatedly beats chest (9,4)

'green space excited' is the definition.
I don't know anything about this answer so I cannot judge whether it can be defined by this definition.

'ape seen within repeatedly beats chest' is the wordplay.
I cannot really understand how this works, but
an anagram of 'ape' is 'eap' which is within the answer.
'beats' could be 'batters' (battering is a kind of beating) and 'batters' is found within the answer.
'chest' could be 'ark' (historical term for a chest) and 'ark' is present in the answer.
This accounts for all the letters.
This explanation may well be incorrect...

Can you help me to learn more?