The most common and most likely answer to this crossword clue is the 7 plus 6 letter word PRAYING MANTIS
I've seen this crossword clue in The Daily Telegraph
P
R
A
Y
I
N
G
M
A
N
T
I
S
More clues leading to the result PRAYING MANTIS
- Sit back after begging chap to find insect
- , 20 Insect makes monk sit up
- Surprisingly, my ant aspiring to be large insect
- Insect making chap at devotions sit back?
- Mary’s painting unusual insect
- Chap at devotions worrying it’s a kind of bug
- Chap in broadcast grips a tiny insect
- Mary’s painting strange insect
Buddy explains!

The straight part
We know that "large insect" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case large insect = praying mantis.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.