It is not confirmed whether Stellar Dawn will have Player Moderators or not, but Mod Markg stated on the official forums (Source) that there most likely will not be any.
A Player Moderator (also known as a Player Mod or P Mod) is a player with additional abilities to help them keep rule-breakers from breaking any more rules. Player moderators' reports have priority over regular players; in other words, Jagex staff look at their reports first. They also have the ability to mute other players for 48 hours and send multiple reports at once (whereas a normal user may only send 1 report per minute). If a Player Moderator talks, they will always be heard, even if a player switches their Public Chat to Off. The only way to not see a Player Moderator's chat in the Chat Box is by completely filtering it out (by click another chat button).
A player moderator is not a Jagex employee. Therefore, they are still subject to the same rules as a normal player. As well as this, they receive no extra benefits, either in game or real life as a result of being a moderator. You should never give a player moderator your password, even if they ask for it, and if you see a player moderator breaking any rule, they should be reported.
Player moderators will always have a silver crown () next to their name when they talk in game. This crown cannot be removed, and there is no crown shown for player moderators on the forums. The only exception to this are Dual Moderators who have green crown () when posting on Forums. If a player without a silver crown beside their name claims to be a player moderator, they should be reported for Rule 5. Similarly, if a player claims to know a Player Moderator and uses this in an attempt to persuade a user one way or another, or attempts to scam or hack the player, they can be reported under the same rule.