What will King Charles want his crowning achievement to be?

It’s difficult not to be nervous in your first few days in a new job – especially if that new job is to become king. True, King Charles III has been training for this moment for all his 73 years, and there is plenty of goodwill. But the challenges are plentiful, too.

So far things have gone well. In his first speech he praised his "darling mama" for "a life well lived". He managed to bring his family together, including those supposedly feuding sons, William and Harry. He also issued a regretful apology to the charities he has supported, saying, quite reasonably, that "it will no longer be possible for me to give so much of my time and energies to the charities and issues for which I care so deeply. But I know this important work will go on in the trusted hands of others".

Now comes the difficult bit. How do you follow the longest-serving British monarch in history, while bringing something new and fresh to an ancient institution? Some priorities – which are full of opportunities as well as potential pitfalls – are already clear.

King Charles’s first priority is the union of the United Kingdom. This has grown increasingly fractious over the past 20 years. The monarch has an important role, though it is a subtle one. King Charles is a figurehead and symbol of unity, but he cannot solve political problems.

A second opportunity is leading the 54 nations of the Commonwealth. The British monarch is head of the Commonwealth and head of state of some Commonwealth nations. The organisation brings together north and south, rich and poor, from every continent except Antarctica. Following the humanitarian disaster of the floods in Pakistan – a Commonwealth country – King Charles could emphasise the ways in which the Commonwealth can bring diverse nations together in a time of need, to help those suffering from the consequences of climate change, poverty and migration.

And that’s where the third opportunity may be important. As Prince of Wales, Charles was a champion for environmental issues long before they became fashionable.

One small personal example came almost two decades ago, when I was making a BBC radio documentary series. I was invited to go with the prince on a factory visit in the Highlands of Scotland, near Balmoral where Queen Elizabeth spent her last days. Charles wore the kilt, in deference to Scottish tradition, and spoke warmly with workers in the factory that made organic biscuits. He made it clear how proud he was that ideas of organic farming – which he had championed for years and which were once at best eccentric and at worst plain crazy – had now become mainstream. The result was new jobs and new products made in Scotland.

The next few days will see King Charles as someone who can bring people together, beginning in religious services and ceremonial occasions in Edinburgh, Belfast, Cardiff and London. But keeping the United Kingdom together is not in his gift. The union depends much more on the attitude of Prime Minister Liz Truss, who has a fractious relationship with the main political party in Scotland, the Scottish National Party. She once clumsily said that she intends to "ignore" the democratically elected First Minister of Scotland, Nicola Sturgeon, who Ms Truss claimed was an "attention seeker". There are other intractable problems with the union, too, especially in Northern Ireland.

Yet for King Charles, the opportunities outweigh the difficulties.

More than 100 years ago, then US president Theodore Roosevelt called the American presidency a "bully pulpit". Roosevelt meant that he had the power to preach and change people’s minds and behaviour. A hereditary monarch like King Charles does not have a direct mandate from voters, yet he does indeed have a "pulpit" and also an attentive audience. Most of all he has an issue, a long history of caring about the environment and a liveable planet.

This is a great opportunity for King Charles to rise above partisan politics as a champion of global green issues, organic farming and diverse wildlife. His voice on global warming and the need to prevent climate-related disasters would echo from the Scottish Highlands to the flooded plains of Pakistan and the bushfires of Australia. In a diverse Commonwealth and an often divided world, King Charles III could surely be a uniter not a divider.

There, however, remains one further problem. When the mourning for Queen Elizabeth ends, there is going to be a prolonged period of reflection about the UK and our place in the world of the 21st century. One piece of good news is that in the month of September 2022, we have peacefully changed our head of state and also changed our head of government, finding a new prime minister in Ms Truss. Ms Truss has then changed personnel in the top level of our government.

But the only people who voted on any of this are about 140,000 members of the Conservative party, not our 68 million other citizens. The system appears to work, but it’s an odd way to run a democracy.