After Republican nominee Donald Trump's shock victory, law firm leaders are grappling to work out what it will mean for business and for the legal profession.

Trump defeated Democrat veteran Hillary Clinton after winning key swing states including Florida, Ohio and North Carolina. His inauguration as the 45th President of the US is set to take place in January next year.

Law firm leaders and partners differ over whether the result represents a bigger challenge for law firms than the uncertainty unleashed by the UK's Brexit vote this summer. Macfarlanes senior partner Charles Martin says: "This has the potential to be bigger than Brexit," while Fieldfisher managing partner Michael Chissick says the result "dwarfs Brexit". But others, such as Travers Smith managing partner David Patient disagree: "The much bigger issue is Brexit and how that plays out."

There is some consensus that the implications for business, due to Trump's background as a real estate mogul, will be less severe than for politics. Where all are agreed though is that, combined with Brexit, the inevitable uncertainty that will follow could have a negative impact on deal flow and trade activity, even if Trump does not follow through with his campaign statements.

Reaction from the market

Charles Martin, senior partner, Macfarlanes

"We need a bit of time out for people to get their heads around all this. We need to understand better than we do what he's actually going to do, out of all the things he set out during his campaign. You'd like to think that some of it on the trade and diplomacy sides would, at the very least, go on the back burner. On the other hand, you can see from the UK's experience on Brexit that those who voted for him will hold him to account, so there will be some tension between what was said and what plays out.

"For the legal world it's all about the implications for our clients. As we've seen with Brexit, you'd expect the impact to be both uneven and unpredictable. We're currently only in the foothills of Brexit – we have a mountain range to climb. I think this has the potential to have a bigger global impact than Brexit – it all depends on what it does to the world order in terms of diplomacy and trade. There is also a cumulative effect. You have the chilling effect on trade of what's happening with both Brexit and now Trump, as well as potential political knock-on effects in other places, especially in continental Europe. Who knows where that takes you? "

Lee Ranson, managing partner and chief executive elect, Eversheds

"A number of the campaign pledges he made were reckless, to say the least. However, I hope and expect that the reality will be somewhat different. As he was keen to remind us, he has many years' experience as a businessman, is a pragmatist and able to get deals done. Let's all hope that that proves to be the case.

"The initial markets' reaction was strong, however, I think things will settle quite quickly. The Republicans are a well established political party who purport to have businesses interests at their core. Mr Trump will need to work with and through Capitol Hill in a cohesive way."

Charlie Geffen, London corporate chair, Gibson Dunn 

"The political consequences are much more significant than the economic consequences – he's a business person. One does lead to the other though, so it will take time for people to have confidence in the policy direction and this is another layer of uncertainty that's unwelcome and could affect activity levels. "

Nick Buckworth, London managing partner, Shearman & Sterling

"As a firm that is very focused on international cross-border transactions, we will keep a close eye on how the US continues to engage in its international trade relations. Donald Trump has expressed certain views on international trade, so we'll see how things will adjust."

Joe Andrew, global chairman, Dentons

"Just like with other elections, you've seen some industries succeed and some not. Some M&A activity will move forward, in areas that are part of Trump's agenda such as infrastructure: that will continue. But there will be many deals around the world where people will pause. A lot of transactions that deal with Latin America will pause for a second.

"The vast majority of our business is domestic or inside Latin America. I think if you have an outpost office there, this could create a temporary slowdown. But I think we will have an advantage as it means money in Latin America is more likely to turn to domestic deals."

Mike Goetz, London managing partner, Ropes & Gray 

"It is too early to formulate what it all means – it doesn't make sense right now. Generally speaking, Republican presidents are viewed as good for business in the US. Assuming that Trump gets into that 'business-friendly' category, people aren't going to be too concerned. It's like Brexit – it will take some time for people to absorb it and understand what the implications are."

Nicholas Cheffings, global chairman, Hogan Lovells

"Once again, a popular vote has defied predictions. The combination of this result and Brexit means we expect to be busy advising clients around the world on the likely policy implications and changes in the regulatory environment. Our transatlantic capabilities and our strong regulatory practice in Washington DC mean we are uniquely well placed to do that. As with Brexit, we have been anticipating this possible outcome and last week we launched an online US election hub for clients."

David Patient, managing partner, Travers Smith 

"We're going to have a period where the uncertainty is unsettling and that could have a depressive effect on deals in the UK but, on the other hand, you could have more people wanting to do more deals outside of the US. For a law firm like ours, apart from the uncertainty and the impact it will have on M&A, it'll just be very small bump in the road, if any. The much bigger issue is Brexit and how that plays out."

Michael Chissick, managing partner, Fieldfisher

"I think this dwarfs Brexit. This is the world's biggest economy and job, and the ramifications are huge. We have an office in the Silicon Valley so it does matter how it all functions. We have to wait and see. Business will go on I believe, in much the same way as after Brexit, which we thought would be the end as life as we knew it. Life goes on. People who do business on the US east and west coast will be less likely to retrench into a US-centric view of the world. Activity levels will go on. The US will remain the largest economy, even under President Trump."

James Palmer, senior partner, Herbert Smith Freehills

"What we're seeing is the first real reaction in the West against globalisation. This and Brexit are part of a broader step back from globalisation, which we started to see the signs of post-financial crisis. But it can't halt globalisation – the speed and access to information and technology is going to continue, despite these setbacks. The unexpected now happens – it isn't over and we shouldn't ignore it, but globalisation isn't reversible. There has always been more instability in the world than we tend to assume."

Paul Rawlinson, chairman, Baker & McKenzie

"As a firm, we play a long game and our decades of advising clients navigating the global economy means we are used to dealing with volatility, whether it is Brexit, instability in emerging markets or other macro geopolitical issues. President-elect Trump's views on trade are one area that our clients will want us to watch closely but it is too soon to say what the impact will be on NAFTA or other agreements. However, we hope we don't see a retreat into an overtly protectionist America – as we would say for any major market internationally. That would be bad for the US and global economies."

US law firm partner 

"Globalisation has left a huge wave of people behind and they're rebelling. Hopefully the political systems now, unlike in the 1930s, will be robust enough to get us through this. It'll be a tough time. Populism has won and we have to live through it."

• For more, see: 'The combination of this and Brexit means we expect to be busy' – Trump victory set to reshape regulatory landscape