Unfortunately you can't do this. Vue's v-html directive binds the content as raw HTML, rather than vue template syntax like you would normally use, which means vue does not interpret any data bindings, such as events. From the vue guide:
The contents of the span will be replaced with the value of the
rawHtml property, interpreted as plain HTML - data bindings are
ignored. Note that you cannot use v-html to compose template partials,
because Vue is not a string-based templating engine.
Also, it's generally considered something to avoid as this would leave your website open to XSS injection unless you're very careful about how you use the v-html property and make sure it never touches user inputted content.
Your best bet would be to parse the data into an object or array as needed and have that be handled by a component with a v-for loop or similar, the data being passed as a prop.
E.g. you might have something like this:
[{text: "Some text content", link: ''},{text: "Followed by a link.", link: "example.com"}]
And have the component operate over that with a v-for and then generate either plain text or an anchor tag depending on the link contents, or whatever other properties you would want to define, such as emitting a specific event with $emit('eventName') which you can capture where the component is called.
