Repurposing a domain

Hi everyone. I am planning on buying an aged domain for a business. The problem is that the domain already has some links - but - to a different industry.

Imagine someone buys a domain of domino's pizza but plans to sell domino game from there.
They will have a bunch of old inbound links from pizza / food websites and with pizza keywords. Nothing related to games or dominos.

That is similar to my situation.

Does anyone have experiences from similar projects or heard from Matt Cuts and his "gang" on this?
How bad will those old links influence the new site?