Determined, he got through to the paper (5)
I believe the answer is:
sheet
'to the paper' is the definition.
(sheet is a kind of paper)
'determined he got' is the wordplay.
I cannot really understand how this works, but
'he' is found in the answer.
'determined' could be 'set' ('set' can be a synonym of 'determined') and 'set' is present in the leftover letters.
No letters remain.
This explanation may well be incorrect...
'through' is the link.
Can you help me to learn more?
(Other definitions for sheet that I've seen before include "Piece of paper, linen, or water" , "Piece of paper or bedding" , "Page of postage stamps" , "leaf" , "Piece of paper; nautical rope" .)