The most common and most likely answer to this crossword clue is the 10 letter word ORTHOPTERA
I've seen this crossword clue in The Times
O
R
T
H
O
P
T
E
R
A
More clues leading to the result ORTHOPTERA
Buddy explains!

The straight part
We know that "the cricket class" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case the cricket class = orthoptera.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 ORTHOPTERA mean?
ORTHOPTERA noun- Any of very many four-winged insects, of the order Orthoptera, such as grasshoppers, crickets and locusts