If Donald Trump decides to invade Greenland, then US forces could use military facilities on British territory, both within the UK and on Overseas Territories.
In order to dissuade US aggression against a British ally, as UK Prime Minister you must make it clear that you will not allow the American military to use British assets, including air and naval bases, and communication hubs such as the GPS antennae based on British Overseas Territories.
Trump is a bully. And the only way to deal with them is to stand up to them. You need to face him down. Take courage from the fact that Trump often chickens out, and we can make him do so again.