Heather Younger's book, The Art of Caring Leadership, offers 9 key aspects to consider, and a free assessment to quantify what appear to be qualifying character traits.
What I love about the book is that the expectation isn't for every leader to be caring in the same way. Heather knows that each of us must be true to ourselves in how we lead, while being self-reflective enough to know when we're getting in our own way, and making gradual, consistent adjustments when necessary.