The most common and most likely answer to this crossword clue is the 3 plus 7 letter word RUN ERRANDS
I've seen this crossword clue in The Times
R
U
N
E
R
R
A
N
D
S
More clues leading to the result RUN ERRANDS
Buddy explains!

The straight part
We know that "Be sent around" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case be sent around = run errands.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.