Engrossed by (4)
I believe the answer is:
into
'engrossed by' is the definition.
(I've seen this in another clue)
This is the entire clue.
(Other definitions for into that I've seen before include "Taking a lively and active interest in (colloq.)" , "Involved with" , "Expression of division" , "Liking" , "ignition regularly missing" .)