If my old Mac has a virus, will it transfer to my new Mac?

Malware, possibly, but not a virus.

Many here suggest installing and running Malwarebytes, but before you do that the least invasive option is to follow the instructions provided by a senior member of this community, John Galt. His user tip here has a set of simple instructions to remove this piece of adware.

Once that has been successful you then can happily transfer your data to your new Mac.

I have no other solution I'm afraid. Perhaps someone else passing by might.

However, I did find this thread from a couple of years ago which offered something else. The post by Linc Davis seemed hopeful.

Sorry Chris88M, I missed your earlier post. The contents of the folders in your screen shots seem not to have anything untoward, so I would go on to the next step of running a check in Malwarebytes. It's always good to do the least intrusive option first.

I've removed a search engine URL hijacker from a Mac with Malware bytes and it takes only a few minutes.