The most common and most likely answer to this crossword clue is the 7 letter word THOUGHT
I've seen this crossword clue in The Times
T
H
O
U
G
H
T
More clues leading to the result THOUGHT
- Leaders of town hall are supposed to provide idea
- Brain activity, however tortuous at first
- Idea — but little time
- Judged, even if finally innocent
- Thinking process however needs time
- But atheist finally believed
- Half of them should care
- Sympathy for all that trouble with foreign money lost
- Initially, Huxley should get consideration
- In difficult time husband will be believed
Buddy explains!

The straight part
We know that "believed" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case believed = thought.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 THOUGHT mean?
THOUGHT verb- To ponder, to go over in one's head.
- To communicate to oneself in one's mind, to try to find a solution to a problem.
- To conceive of something or someone (usually followed by of; infrequently, by on).
- To be of opinion (that); to consider, judge, regard, or look upon (something) as.
- To guess; to reckon.
- To plan; to be considering; to be of a mind (to do something).
- To presume; to venture.
- To seem, to appear.
- Form created in the mind, rather than the forms perceived through the five senses; an instance of thinking.
- The operation by which such forms arise or are manipulated; the process of thinking; the agency by which thinking is accomplished.
- A way of thinking (associated with a group, nation or region).