As I said in the description, there's none in captivity at the moment but they've been kept a fair few times in the past, especially in Australia and New Zealand and most recently by Taronga Zoo (see images below, held them for decades but the last one died in 2014). The reason there are none in zoos (or aquariums) at the moment is not because they can't be held there, they seem to do well enough, but because they're so hard to source - given capturing them from the wild in Antarctica is obviously off the cards (it'd be unnecessarily difficult both logistically and legally), their only option to enter captive care is when they wash up on the southern continents in need of rehab. Sometimes, these individuals cannot released after being raised back to health due to concerns that they could spread diseases to the wild population, and this is how they tend to end up in zoos.
They're a species that has a history in captivity and is also a realistic choice for zoos set in Australia, New Zealand, South Africa or Patagonia (the places most likely to be visited by vagrant leopard seals), and this combined with the fact they're one of my favourite animals means I can't help but wish for them.