My suggestion is to use best practices for user story creation, like to follow the INVEST principle, also you need to have Grooming sessions for your stories which would go into sprint. You should practice static testing of your available design documents and available requirement - while doing that you could find missed requirements. Try to create FAS (feature analysis specifications). Also you can try to assign a role of requirements analyst to one tester or dev.
In short, it all depends of what sdlc/stlc you are following.
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