Your gut feeling is pointing you in the right direction, toward the practice of full kitting tasks before those tasks are initiated.
Essentially, full kitting means that all of the inputs requires to complete a task are collected into a set before that task is initiated. Inputs can include information (manuals, instructions, data), physical materials, tools that will be used to do the work, and the availability of needed resources and people. I'm having difficulty finding a quality, online reference to link to. Kitting is a concept used in both Theory of Constraints and Lean methodologies.
Some tools for kitting in software projects include:
- Public source code repositories like GitHub or GitLab
- Wikis for documentation
- User stories with acceptance criteria
- Wireframe user interface mockups
- Links to deployed web services
All of the above can be associated with a Jira task as it moves through your team's workflow, either as an attachment or linked resource. This approach will likely work with other software too if your team chooses a different took than Jira. Some software, for example Kanbanery, will allow a task to be marked as "ready to pull" meaning that all elements of the kit have been collected and the task is ready for a team member to begin working on it.