Click on the icon on the top right of your screen that looks like a person. There it says "next level requirement". If it says "mission" than you gain a level after you do a SP mission. If it has a dollar amount than you have to gain that much in cash value to go up a level. When you go up the level, the SP campaign will kick back in and you'll be contacted.

Me no gun

If the Player Stats screen says "mission" for the next requirement, then Juni should have contacted you already.. so I suspect you're seeing a $ ammount. Once you reach that ammount (and that's total worth, not amount in your 'bank') you'll get the next level, and then Juni was automaticlaly contact you the next time you launch into space.