There's a pay range for each level, so you will definitely get a raise when moving up a level/multiple levels, but in my experience where you fall within that range will vary from person to person, depending on several different factors. Myself and another associate in my department got moved from II to IV recently, but our raises were definitely different. Also, with your experience and the fact that you've been a specialist in the past, you could try asking for a promotion to a level IV at your current position, as opposed to applying for a different one. That's the route I had taken, and if they're willing to work with you it's much easier than going for a whole other position.