I would not train a client without it! And I always mention it to new or potential clients when they start training with me. I want them to know that I’m as serious about this business as they are.
Also, if you’re training out of your home or theirs, make sure that your homeowners policy is up to date as well. I check my liability insurance against my homeowners policy to make sure that both my home office, equipment and myself are always covered no matter where I train clients.
If you’re training out of another facility, see if you can get it listed or yourself listed on their facility insurance. Sometimes you can, sometimes you can’t. But it doesn’t hurt to ask. And don’t assume that a facility will add you to their insurance. I always carry liability insurance on myself regardless of what the facility says. I need to make sure that I’m covered if anything should go wrong.