Finish terrible poem about Celt (8)
I believe the answer is:
complete
'finish' is the definition.
(I know that complete is a more specific form of accomplish)
'terrible poem about celt' is the wordplay.
'terrible' is an anagram indicator.
'about' means one lot of letters go next to another.
'poem' after 'celt' is 'celtpoem'.
'celtpoem' is an anagram of 'COMPLETE'.
(Other definitions for complete that I've seen before include "Finish; whole" , "Finished, entire" , "Whole and unabridged" , "Bring to a finish" , "Finished - whole" .)