The most common and most likely answer to this crossword clue is the 6 letter word ENFOLD
I've seen this crossword clue in Financial Times
E
N
F
O
L
D
Buddy explains!

The straight part
We know that "Wrap up" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case wrap up = enfold.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does ENFOLD mean?
ENFOLD verb- To fold something around; to envelop
- To embrace