The article below from Forbes, offers 13 useful tips for connecting with new prospects.  

I have whittled this down to 7 and given them a modern selling perspective to help you engage with new prospects on social. 

1. Be Curious: Without curiosity, you may leave a stone unturned.  If someone has visited your Linkedin profile, send them a request and start a conversation.   

2. Be Real: Be someone of value and just interact with them. It doesn't matter who you are going after, be a good person and start a conversation with them. Share their content, comment on their posts, ask them questions. 

3. Build Your Brand: A strong sales strategy is to build a brand around yourself and your organisation and product. Position yourself as a subject matter expert in your field and engage in social selling and content dissemination in your network.  Be consistent with posts and comments, this is a daily activity. 

4. Be of value : Work on your industry knowledge, collate a repository of up to date content that you can refer back to or share in your network.  These are nuggets that can help the conversation to get started.  If you have strong industry knowledge or information that can help a prospect, there is a higher likelihood they want to talk to you. 

5 Offer A Very Clear Value Proposition: Your Linkedin page can articulate your value proposition.  What is it that the prospect will get from doing business with you, and why you? 

6. Market First, Sell Second: Customers are much further down the buying journey and are more educated than ever before by the time they get to a salesperson.

7. Take the conversation off line: When you have the chance, take the conversation off line. Use social to connect with a wide range of people in your prospects.  Then when you are on next on site, go and introduce yourself.