Keen on opening piece right away (4)
I believe the answer is:
into
'keen on' is the definition.
(I've seen this before)
'opening piece right away' is the wordplay.
I cannot really see how this works, but
'piece' could be 'n' (abbreviation for Knight in chess notation) and 'n' is found within the answer.
The remaining letters 'ito' is a valid word which might be clued in a way I don't see.
This may be the basis of the clue (or it may be nonsense).
Can you help me to learn more?
(Other definitions for into that I've seen before include "Taking an active and lively interest (in something)" , "Keenly interested in" , "Enthusiastic about" , "Keen on, colloquially" , "digging" .)