The most common and most likely answer to this crossword clue is the 4 plus 6 letter word NAIL BITERS
N
A
I
L
B
I
T
E
R
S
Buddy explains!

The straight part
We know that "moments of great anxiety" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case moments of great anxiety = nail biters.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 NAIL BITERS mean?
NAIL BITERS noun- One who bites or chews his or her fingernails
- A nervous or uncomfortable situation
- An engaging or exciting cliffhanger.