The most common and most likely answer to this crossword clue is the 7 letter word BELIEFS
I've seen this crossword clue in The Guardian
B
E
L
I
E
F
S
Buddy explains!
The straight part
We know that "Number of convictions" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case number of convictions = beliefs.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 BELIEFS mean?
BELIEFS noun- Mental acceptance of a claim as true.
- Faith or trust in the reality of something; often based upon one's own reasoning, trust in a claim, desire of actuality, and/or evidence considered.
- Something believed.
- The quality or state of believing.
- Religious faith.
- (in the plural) One's religious or moral convictions.