Speaker’s fully absorbed, stuck into paper (7)
I believe the answer is:
wrapped
'stuck into paper' is the definition.
'speaker's fully absorbed' is the wordplay.
'speaker's' indicates a 'sounds like' (homophone) clue.
'fully absorbed' becomes 'rapt' (I've seen this before).
'rapt' is a homophone of 'WRAPPED'.
(Other definitions for wrapped that I've seen before include "Enclosed, swaddled" , "Like many a present" , "Enfolded - swathed" , "Put in envelope" .)