The most common and most likely answer to this crossword clue is the 9 letter word REASSURED
I've seen this crossword clue in The Daily Telegraph
R
E
A
S
S
U
R
E
D
More clues leading to the result REASSURED
Buddy explains!

The straight part
We know that "Relieved from anxiety" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case relieved from anxiety = reassured.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 REASSURED mean?
REASSURED verb- To assure anew; to restore confidence to; to free from fear or self-doubt.
- To reinsure.