More embarrassed about English game (3,4)
I believe the answer is:
red deer
'game' is the definition.
The definition and answer can be both animals as well as being singular nouns.
Perhaps you can see an association between them that I don't see?
'more embarrassed about english' is the wordplay.
'more embarrassed' becomes 'redder' (someone may go red from embarrassment).
'about' means one lot of letters goes inside another.
'english' becomes 'E' (abbreviation).
'redder' enclosing 'e' is 'RED DEER'.
Can you help me to learn more?
(Other definitions for red deer that I've seen before include "Large-antlered animal" , "Exmoor fauna, say" , "Large grazing animal of temperate Europe and Asia" , "Does perhaps" , "source of venison" .)