Can my employment agreement be transferred to new employer?

Hi all

In a pretty messed up situation atm, well it feels like it. The owner of the company I work for has sold it to a new owner in the form of an asset sale, it doesn’t settle for another month, I have been formally notified of the sale - though not formally offered a new position yet, I expect that will come soon.

The issue is, that I had signed an employment agreement at the start of my employment many years ago that had a restraint of trade clause in it, and the clause explicitly states it can be transferred to any entity or company.
Now that it’s been sold, and having met the new owners, I don’t wish to continue working there as I don’t feel my plans align with theirs.

But, in my industry it’s common for employees who leave to work for another company are often threatened with legal action when they attempt to solicit former clients. Mind you, these clients are my clients, and have never met nor spoken to my former employer or new employer.
Can my former employer really assign the rights to my employment agreement, and the restraint of trade, to this new employer without my consent?