A great framework for delegating work or encouraging a team member to identify and own new work:
Challenge people to operate at the next level and promise support for them taking on that challenge.
Example: someone says that they are identifying a problem that is a bit of a stretch for them to carve out or solve. You can identify it as a challenge for them and offer it to them as a challenge that they can accept. And you should communicate that you will support them taking on that challenge (and how you’ll support them).
Challenge and Support