The most common and most likely answer to this crossword clue is the 11 letter word BABY-SITTER
I've seen this crossword clue in Financial Times
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More clues leading to the result BABY-SITTER
Buddy explains!
The straight part
We know that "One minding small issue" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case one minding small issue = baby-sitter.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 BABY-SITTER mean?
BABY-SITTER noun- A person who cares for one or more babies or children for a short period of time in place of their legal guardians.