First four in line over 21 are Counsellors of State unless they are the heir apparent who becomes one at 18.
Charles - aged 18.
William, Harry and Andrew all at 21 (as did Edward and Anne and the others before them such as Margaret, Richard of Gloucester, Edward of Kent etc)
When the Queen first became Queen the Counsellors of State were - Margaret, Henry of Gloucester, Princess Mary and the late Earl of Harewood.
As others ahead of these in the line of succession turned 21 the last one dropped off e.g. Edward of Kent replaced the late Earl of Harewood, in 1957, and the following year Princess Alexandra replaced Princess Mary.
The only Counsellors of State who isn't in the first four is the consort of the monarch and the consort of previous monarchs e.g. Philip and The Queen Mother.
When the Queen passes Beatrice will step up and be the fourth CoS until either this new baby turns 21 in Charles' reign or it turns 18 in William's reign but she may have to return to the position for a year or so at times as well, depending on when those ahead of her die, like Richard of Gloucester had to do in the 60s and early 70s.
Although Philip is eligible he has actually never served because everytime the Queen has gone overseas he has gone with her and so has been out of the country.