Building on the excellent advice from the other mentors, consider how you are going to present your case for promotion and support. You need to think and communicate in ways that "speak the language" of your audience. It's likely that senior leadership thinks in terms of ROI...what are they getting for their investment? Some people respond more to risk or cost...what will it cost the organization if you don't have the ability to lead and fulfill YOUR role?
Your proposal should address both risk and rewards.
This is essentially a sales job. You have to understand your clients' pain or concerns and how you will help address that. It may be a staged process where you are looking to get agreement on a number of facts before making a case for your promotion and support. If you can get your hands on the leadership team's strategy and SWOT analysis, you'll have information for your case. Using a few visuals like graphs (increased number of employees over time, sales or client stats, turnover stats, industry trends, gap analysis ) will help tell the story. Talent retention and succession planning have cost/benefits that you can track or get stats for.
Present facts and information that senior leaders agree on:
Context: Growth in company, trends, successes, etc
Current situation: turnover rates, new skills needed, workforce trends
Tension points: "misses" with clients, aging workforce (especially on leadership team), new regulations, client needs, etc
Ask questions: How does leadership intend to address tensions and gaps? What are their visions for the company? What support do they need to fulfill the vision?
THEN make a case for your promotion and support as a way to address THEIR issues and tensions.
Obviously, this is a simplified overview of what you might do since I don't know your actual situation. I hope it is helpful.