Start by reviewing your company process for performance management. Then follow it. At each step notify HR of your intentions. Document all meetings you have with the individual concerned and HR.
Set clear achievable short term goals with the individual that enable you to clearly identify and articulate their poor performance. Use that to reiterate performance expectations. If performance doesn’t improve, begin escalating with HR support (by that I mean tell them what you intend to do next and get them to sit in on formal meetings).
Having been through this myself it’s about ensuring it isn’t a surprise to the individual concerned that their performance is poor and creating the evidence that you followed a reasonable process leading up to any termination because worst case you and the Company end up being taken to employment tribunal. And that’s where your thorough notes and evidence that HR were advised on the steps you were planning to take are key.
And as a manager you have to pursue this because the wider team will know who’s not performing and be watching to see how the business addresses it. If you’re lucky the individual will decide to leave once they realise the direction of travel.
Good luck. And I recommend the book “Radical Candor”