The most common and most likely answer to this crossword clue is the 11 letter word REASSURANCE
I've seen this crossword clue in Financial Times
R
E
A
S
S
U
R
A
N
C
E
Buddy explains!
The straight part
We know that "that allays doubts" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case that allays doubts = reassurance.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 REASSURANCE mean?
REASSURANCE noun- The feeling of being reassured, of having confidence restored, of having apprehensions dispelled.
- The act of confirming someone's opinion or impression.
- Reinsurance.