Knowing the domain name, would be the best. I would look at
Semrush Rank, Alexa Rank, SimilarWeb traffic, seo parameters from Ahrefs.com, and Majestic.com, number of pages indexed in Google and Bing, and other things like that. It would be good to look at the website too, how it is constructed, what are the categories, and internal linking, and other things like that.
You said, that the website has links, and authority, and if this is really the case, this can have a lot of financial value. I guess your goal would be to use this to make money, and it could be a lot better to keep the current site as is, and start with a new one, and link to it from this one, lets say.
Either way, deleting a site with a lot of backlinks, and starting putting something else on this domain, does not sound like a good idea, unless we are talking about a domain like porn.com, sex.com, or something like that. Even then, this would need to be looked into, and planned, and possibly kept as is too.
Edit: Even if you have something like CelebNudes.com, registering something like HotCelebNudes.com and working on that, would not make a lot of a difference.