Best way to fix incoming 404 links on an Expired Domain?

I had a site on an expired domain that had a lot of backlinks from various sites and they were resulting in 404s. I recently rebranded that old site to a new domain (again an expired one) and now they have even more 404s combined.

Could you guys tell me what's the best way to fix 404 links? Should I redirect them to the homepage?

I am seeing a lot of traffic drop after rebranding. Assuming these 404s are one of the reasons for the drop.

Please help.