The world is in a very different place to what it was when Trump was last in power. The global move to renewable energy is now happening at an unprecedented pace. Nothing the US government can do will change the simple fact that renewable energy is cheaper and more reliable than oil, gas and coal. Fossil fuels are a thing of the past. The world is moving on.
The US has never been a great team player at COPs, regardless of which party is in government. People don’t go to COPs expecting the US to push for more ambition. When Trump quit the Paris Agreement in 2016, many governments still stuck to their plans. As always, other countries need to step up at COP29.
Trump can deny climate change all he wants, but the laws of physics don’t care about politics. As we speak, nearly every US state is experiencing drought and last month, back-to-back hurricanes wreaked havoc in the southeast. Extreme weather will keep getting worse in the US as long as the world burns fossil fuels.
 

Donald Trump has won a historic second term as US President and this will have a profound impact on the domestic and international climate change agenda. Trump declared during his election campaign that he does not believe in climate change. During his first term in office, he withdrew the US from the Paris Agreement and many of us predict he will do this again.  Pulling out one of the world superpowers from COP negotiations to reduce global greenhouse gas emissions is a big deal – as it allows other countries to slow their own decarbonisation and blame the US instead of their own lack of ambition.    
Domestically Trump is a vocal supporter of coal, but coal use decline during his first Presidency due to the switch to gas and renewable energy.  This has continued under President Biden and will continue into the future due to simple economics.   This reflects global trends moving away from coal to natural gas and renewable energy.  But the transition from fossil fuels is to slow and the UN have suggested that with current trends we are looking at 3.1˚C warming by the end of the century. 
The other major trend that Trump has little influence on is the growth in the global green economy which is worth over $10 trillion annually which is 10% of the world’s GDP. In the US there are at least 10 million jobs in the green economy compared with 300,000 in the fossil fuel industry.  Hence, if you want to grow your economy and make jobs, then investment in the green economy will be essential. 
In summary Trump may slow down the transition away from fossil fuels and allow other countries to delay action – but the writing is on the wall both politically and economically for fossil fuels.  It is when - not if - fossil fuels cease to be used as an energy source.
 

Donald Trump said relatively little about climate change on the campaign trail, except occasional comments that showed he still does not understand the damage it is causing to lives and livelihoods in the United States. Based on his first term, we can expect him to withdraw the United States from the Paris Agreement and fail to honour commitments to provide financial support for poor countries to deal with climate change, which is the main issue due to be discussed at the United Nations climate change summit in Azerbaijan next week. He may not reverse the investments in clean energy technologies that have resulted from the Inflation Reduction Act because they have benefited many Republican states, but he had pledged to introduce heavy tariffs on imports of cheap Chinese electric vehicles, which will increase prices for American consumers. Mr Trump is also being advised by some Republican groups to abolish the National Oceanic and Atmospheric Administration, including the National Hurricane Center, which would leave the United States much more vulnerable to extreme weather.

We can say goodbye to the Paris Agreement goal of limiting warming to 1.5 Celsius above pre-industrial levels. Increasingly deadly climate impacts will escalate. It is as simple as that. The floods and the droughts and the heatwaves, the devastated lives and destroyed crops, these will not stop for a climate denier. But more positively, international cooperation will also not stop for a climate denier. The ongoing energy transition to renewables will not stop for a climate denier.  The US has voted to continue its long-term loss of power internationally as it backs fossil dinosaur industries and not those of future growth and prosperity.

Trump’s re-election may surprise on climate. Internationally, Trump may withdraw the US from the Paris Agreement for a second time, but that’s not likely to have the sort of impact it did before in terms of international diplomacy. It’s already more or less priced in. Other countries will carry on without the US. 
Of course, US climate emissions still count for a big slice of the global whole, so what he does domestically on climate also matters. The Biden administration was itself no angel on climate – US fracking continued apace, and exports of LNG reached record highs. Biden did act to reduce methane emissions though, which is critical for remaining below 2 degrees of warming because it’s a very powerful short term greenhouse gas. Trump could be tempted to cut back on those methane rules. But the EU’s new methane law will not allow imports from countries which have weak methane controls, and the UK should be looking at doing something similar with its proposed CBAM (carbon border adjustment mechanism). Trade is one of Trump’s favourite policy tools, but it can also be used against him if he tries to engage in a climate race to the bottom.
As other have noted, US climate policy has also largely moved from stick to carrots in the shape of IRA subsidies for climate friendly industries. These will be harder to dismantle than rule-based sticks because industries like freebies and many of them go to Republican states. 
Likewise, politicians like Trump are elected for a relatively short term, but the markets invest for periods beyond this. So, US industry will be positioning itself for a decarbonised economy. It won’t be investing in coal. And demand for oil and gas will fall as electrification proceeds.
The real question is whether that decarbonisation and electrification will take place despite Trump of because of him. With Elon Musk’s role in the election, we may see a push to position the US as a new energy powerhouse, with a great lithium industry, a resurgent nuclear industry, and an internationally competitive EV auto and battery industry. Trump is a businessman. And he likes to win. Sticking to a fossil fuel economy is not likely to position the US economy for the win. So that may yet be the surprise on climate in a Trump presidency. This is not climate, this is business.