Starting a New Business While Employed FT

I work a contract job full time in tech and am starting a new business on the side in a totally different industry.

My current employment contract states I must get “permission” to work another job or start a business.

Don't want to do that or let them know what I am working on. I plan on quitting when things pick up a bit.

I am seeing some success with outreach on LinkedIn for my new business but I dont have a LinkedIn company page or the business listed on my profile. I direct people to my website and tell them I am updating my LinkedIn.

I want to add my company to my LinkedIn profile but want to hide it from my employer. I am debating abandoning LinkedIn and use another channel for marketing my services.

Any advice?