Succession to the Crown not to depend on gender
In determining the succession to the Crown, the gender of a person born after 28 October 2011 does not give that person, or that person's descendants, precedence over any other person (whenever born).
Which means that the new Princess of Cambridge (not the first, check out the Grand Duchess of Mecklenburg-Strelitz - can't find a Princess Charlotte of Cambridge - but did find one of Wales, which is what she will become if she does not marry before her father becomes Prince of Wales - she would have come Queen Regnant instead of Victoria, but died aged 21) will be 4th in line to all 16 thrones inhabited by the UK Sovereign regardless of the gender of any further Cambridges:
The action of bringing the change into force was repeated around the 16 realms on 26.3.15 - e.g. Australia:
Succession to the Crown Commencement Proclamation 2015
This instrument commences on the day, and at the time, it is registered.
By His Excellency’s Command
Curiously Canada assented to our Bill rather than make their own, because they didn't think that they had any laws of succession of their own.....although I gather their is legal action....
2. The alteration in the law touching the Succession to the Throne set out in the bill laid before the Parliament of the United Kingdom and entitled A Bill to Make succession to the Crown not depend on gender; to make provision about Royal Marriages; and for connected purposes is assented to.