Relationship management is the last of the seven Quality Management Principles, but in a sense it brings us back to the first one—Customer focus. In the broadest sense, relationship management is about taking care in your interactions with all of the interested parties that affect your work, and your customers are clearly on that list. So you could almost say that customer focus is just a part of relationship management.
In reality we treat customers separately because they are a very special kind of interested party, and because they have some very special needs not shared by the others. Also—speaking historically—the whole concept of Quality grew out of a concern for customer satisfaction. It is the existence of customers that gives us the concept of Quality in the first place, and so it is not unreasonable for customers to have one Principle all to themselves.
But in the long run we do well to nurture relationships with all our interested parties (or all the relevant ones); and this principle reminds us to do just that.
Why bother?
Remember who your interested parties are. ISO 9000:2015 explains that:
The relevant interested parties are those that provide significant risk to organizational sustainability if their needs and expectations are not met. [2.2.4, para. 2]
In other words, these are the people who can ruin things for you. It pays to stay on their good side.
More exactly, you want to encourage them to act in a way that helps you and does not thwart you. But why should they do that? What's in it for them? It is up to you to find a way to appeal to them, so that they see helping you (or at any rate not thwarting you) as in their own best interest. If you can think along these lines consistently—that's relationship management! The rest is just details.
Who is involved?
Anyone who wants something from you. That could include your landlord, your neighbors, and the state revenue office. Mostly you exclude customers, because (as noted above) they are already handled elsewhere. And you want to focus on the ones that pose the biggest risk. For most companies, most of the time, this means your suppliers.
But it might include others as well. Even your competitors can be considered interested parties. That's what trade associations are about, after all: they are venues where competitors can meet to cooperate on common issues, like encouraging a general market for their products. (Someone once quipped, "You have to sell coffee before you can sell Folgers.")
Informally, you probably already know which interested parties matter to your business. Formally, you'll capture a list when you document the Context of your Organization. Whether you need to document them any more extensively than that is up to you. (You may remember that last fall I described a stakeholder matrix which captures a lot of information about each interested party, but it's more than most organizations need most of the time.)
What next?
And after that, it all depends on what you need. A common approach for some companies is to set quality objectives for their suppliers to meet, and then offer support as the suppliers strive to meet them.
Whether this approach will be useful for you depends on many factors, but it is only fair to add that an important one is surely the question, "How much of the supplier's total business do you provide?" If you are a major customer for this supplier, they are likely to want to work with you. If you are a minor or negligible customer for that supplier, they may be less motivated.
It can also happen that your supplier might point out features of your own operations that hold you back. Maybe you ask your supplier what it would take to negotiate lower prices, and they tell you, "All your orders come in as emergency rush jobs with no lead time. Since we can't plan for them, we have to charge you premium prices." That's a sign of a Quality problem in your own operations—namely, that your planning isn't very effective. If you can solve that problem, it will benefit you in dozens of ways not limited to the prices you pay your suppliers!
If you and your suppliers can help each other in even simple ways like this, you have take the first steps towards growing your relationship into a kind of partnership.
Of course you can go farther. You can enter into collaborative relationships with other businesses, if there is value to be had by doing so. There's even a standard to help you define a system for such collaborations: ISO 44001—Collaborative business relationship management systems. But that's not for everyone. As always, it depends on what you need.
Even if you don't need any formal partnerships and aren't interested in collaboration, though, you still need basic relationship management. No company is an island. And if you treat your interested parties like they matter to you, the odds are good that you'll matter to them.