How can I avoid nested ternary expressions in my code?

Yes, but my linter is not happy: 44:16 error Do not nest ternary expressions [no-nested-ternary]

If that's your only problem then the solution is simple. Create your own conditional function:

const iff = (condition, then, otherwise) => condition ? then : otherwise;

props => ({
  iconColor: props.isPriority ?
    iff(props.isCompleted, variables.color.lightpurple, variables.color.purple) :
    variables.color.gray3,
  iconName: props.isPriority ? 'star-full' : 'star-empty',
})

Now your linter shouldn't complain. That being said, you should disable [no-nested-ternary] in your linter. It's kind of stupid that your linter thinks that nested conditionals are bad.