The most common and most likely answer to this crossword clue is the 6 letter word CREDIT
I've seen this crossword clue in The Guardian
C
R
E
D
I
T
More clues leading to the result CREDIT
- Believe in arrangement not requiring immediate payment
- Believe notice about newspaper chief
- Unusually direct source of pride
- Acclaim — Conservative meeting left-winger gets it
- Good reputation: Conservative and Socialist have it
- Believe in not being overdrawn?
- Crossword started— time to have belief
- Chain reaction starts with correct recognition
- Believe journalist struck through review
- Breaking sacred Italian trust
Buddy explains!

The straight part
We know that "Believe" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case believe = credit.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 CREDIT mean?
CREDIT noun- Reliance on the truth of something said or done; faith; trust.
- Recognition and respect.
- Acknowledgement of a contribution, especially in the performing arts.
- (television/film, usually in the plural) Written titles and other information about the TV program or movie shown at the beginning and/or end of the TV program or movie.
- A privilege of delayed payment extended to a buyer or borrower on the seller's or lender's belief that what is given will be repaid.
- The time given for payment for something sold on trust.
- A person's credit rating or creditworthiness, as represented by their history of borrowing and repayment (or non payment).
- An addition to certain accounts; the side of an account on which payments received are entered.
- (tax accounting) A reduction in taxes owed, or a refund for excess taxes paid.
- A source of value, distinction or honour.
- An arbitrary unit of value, used in many token economies.
- Recognition for having taken a course (class).
- A course credit, a credit hour – used as measure if enough courses have been taken for graduation.
- To believe; to put credence in.
- To add to an account.
- To acknowledge the contribution of.
- To bring honour or repute upon; to do credit to; to raise the estimation of.