The most common and most likely answer to this crossword clue is the 8 letter word SURROUND
I've seen this crossword clue in The Sunday Telegraph
S
U
R
R
O
U
N
D
More clues leading to the result SURROUND
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 = surround.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 SURROUND mean?
SURROUND noun- Anything, such as a fence or border, that surrounds something.
- To encircle something or simultaneously extend in all directions.
- To enclose or confine something on all sides so as to prevent escape.
- To pass around; to travel about; to circumnavigate.