I’m guessing “tie you” doesn’t literally mean with rope, unless your job is way more interesting than I think. She’s probably worried about your client being attracted to you and trying to pull you away from her. Which could be a valid concern or could be her being insecure, depending on the situation.
What is this client actually doing? Is she flirting with you, buying you gifts, trying to meet outside of work hours? Or is your girlfriend just seeing a successful woman and feeling threatened? There’s a big difference between actual boundary crossing and your girlfriend’s imagination.
If the client is actually being inappropriate, you need to set boundaries at work. Keep things professional, don’t engage with flirting, maybe even talk to your supervisor if it’s really out of hand. Your girlfriend needs to see that you’re handling it and that your loyalty is to her.
But if your girlfriend is just paranoid and there’s nothing actually happening, you need to address that with her. Constant accusations and suspicion will wear you down over time. Reassure her but also let her know that baseless jealousy isn’t okay. You can’t live your life walking on eggshells around every woman you interact with for work.