The most common and most likely answer to this crossword clue is the 7 letter word CARACAL
I've seen this crossword clue in The Guardian
C
A
R
A
C
A
L
Buddy explains!

The straight part
We know that "Desert lynx" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case desert lynx = caracal.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 CARACAL mean?
CARACAL noun- A type of cat native to Southern Africa, West Asia, and parts of Central and South Asia, Caracal caracal.