The most common and most likely answer to this crossword clue is the 1 plus 6 plus 2 plus 4 letter word A TISSUE OF LIES
I've seen this crossword clue in The Daily Telegraph
A
T
I
S
S
U
E
O
F
L
I
E
S
More clues leading to the result A TISSUE OF LIES
Buddy explains!

The straight part
We know that "Don’t believe them" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case don’t believe them = a tissue of lies.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.