Bound to be stifling in the finish (8)
I believe the answer is:
enclosed
'bound' is the definition.
(thesaurus)
'stifling in the finish' is the wordplay.
'stifling' becomes 'close' (I can't justify this - if you can you should believe this answer much more).
'in' is an insertion indicator.
'the finish' becomes 'end' (I've seen this in another clue).
'close' going within 'end' is 'ENCLOSED'.
'to be' is the link.
Can you help me to learn more?
(Other definitions for enclosed that I've seen before include "Surrounded on all sides" , "Held" , "Inserted with letter" , "Shut up or included in an envelope" , "Surrounded completely, caged" .)