Japanese art almost beginning to entertain a male (7)
I believe the answer is:
origami
'japanese art' is the definition.
(I've seen this before)
'almost beginning to entertain a male' is the wordplay.
'almost beginning' becomes 'origi' (I can't justify this - if you can you should give a lot more credence to this answer).
'to entertain' is an insertion indicator.
'male' becomes 'm' (common abbreviation).
'a'+'m'='am'
'origi' enclosing 'am' is 'ORIGAMI'.
Can you help me to learn more?
(Other definitions for origami that I've seen before include "Jap. paper-folding art" , "Art of crafting objects from paper" , "Japanese paper-folding art" , "Artwork with paper" , "Delicate operations" .)