The most common and most likely answer to this crossword clue is the 13 letter word ORTHODONTISTS
I've seen this crossword clue in The Daily Telegraph
O
R
T
H
O
D
O
N
T
I
S
T
S
Buddy explains!
The straight part
We know that "They should straighten it out" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case they should straighten it out = orthodontists.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 ORTHODONTISTS mean?
ORTHODONTISTS noun- An orthodontic dentist