I would encourage you to think about outreach more broadly than just LinkedIn. While LinkedIn is a great place to find potential customers (sales) and new team members (recruiting).

Many busy professionals require the help of a virtual assistant, or junior team member to help with their outreach efforts. You can make a career out of it if you can master the process, price it appropriately, and provide results in excess of the investment your client makes.

Specific to LinkedIn, this means being able to identify people who fit the description of your clients target market for new sales or team members. It then would become your job to send the initial communications and requisite follow-up messages to either setup an in-person meeting, product demo, or any other objective that your client has.

Simply put, your job would be to expertly handle the manual and emotional labor of finding someone, connecting with them, and achieving an objective with that them on behalf of your client.

Let me know if you'd like to discuss this further on Clarity.