Is this question premature? Oh, absolutely. But let’s take a stab at it anyway.
Let’s start with the issue of the title and move on from there. The most obvious question is whether this child will be a prince or princess, but the answer is actually a bit convoluted (of course!). As it stands today, barring any further intervention, the answer is no. So, let’s dig in:
Back in 1917 George V issued a Letters Patent that essentially stated the great-grandchildren of the sovereign born via a male line would enjoy the same status as any child of a duke, not a prince. In this case, that means that while Elizabeth II remains on the throne, the Prince of Wales and the Duke of Sussex are princes, but the Duke of Sussex’s children are not princes and princesses. They will only hold the rank of a child of a duke.
The only exception to this was the eldest son of the eldest of the eldest son of the eldest son – in this case, Prince George, since he is a future monarch. As the rule stood in 1917, that would mean that while George was a prince, his younger siblings wouldn’t be. This was changed in 2012 when the Duchess of Cambridge was pregnant with George and the Royal Family re-evaluated the succession and rank not knowing if she was carrying a boy or a girl. At the same time that the UK took on absolute primogeniture, meaning that the eldest child – not son – inherits the throne, the Queen issued a Letters Patent that made all of William’s then-future children princes and princesses. Because of that, Charlotte and Louis are thus a princess and prince, respectively.
That decree specifically called out the children of the Prince of Wales’s eldest son – William, not Harry. So, unless the Queen intervenes yet again between now and Spring 2019, Harry’s eldest son would be known as the Earl of Dumbarton, his secondary title, while his daughter would be Lady X Mountbatten-Windsor.
This will change when Charles ascends the throne, at which point Harry’s children will become the grandchildren of a sovereign. Again, barring any intervention, they will become HRH The Prince/Princess X of Sussex.
So, why a possible intervention? Well, it goes back to the idea of a streamlined monarchy that we know Charles – and presumably, William – prefer. For Harry that theoretically means that he will play an increasingly large role through the end of his grandmother’s reign and into his father’s, but it’s anyone’s guess how that will evolve once William sits on the throne. By then, quite a lot will depend on how Harry and the Duchess of Sussex’s royal careers have played out and how old the Cambridge children are.
Likely, the couple will continue to work as full-time royals given their popularity and how close William and Harry are. But that doesn’t necessary extend to their children.
While Harry will eventually become the son of a monarch, it’s worth noting that the highest “status” his children will reach will be during Charles’s reign when they are the monarchs grandchildren. From there, they will continue to recede into the background. Princess Margaret’s children are a point of comparison, though they weren’t alive for their grandfather’s reign. The current Dukes of Kent and Gloucester, Princess Alexandra and Prince Michael of Kent are still more examples – all are grandchildren of George V, but mostly unknown to the public today and considered minor royals during the reign of their cousin, Elizabeth II.
Princess Margaret’s children are notably not royal, however their rank is due to the fact that their “royal blood” is through their mother, not their father. Margaret’s son, David, is now the Earl of Snowden, having taken on his late father’s title (one handed out by the Queen in 1961).
Similarly, the Princess Royal’s decision to keep her own children non-royal is not a direct comparison given that their ties are also through their mother. Even more, Anne pointedly opted not to have either of her husbands taken on a title that could be inherited by children…presumably with their buy-in, but you never know with Anne 😉
The best comparisons are the Duke of York and the Earl of Wessex – or Princes Andrew and Edward, the Queen’s younger sons. They hold the same rank that Harry will someday hold when Charles is on the throne, but interestingly, they took very different approaches to how to incorporate their children into the public side of the Royal Family.
Andrew married in 1986 and his two daughters, Princesses Beatrice and Eugenie, were born in 1988 and 1990. Those were very different days from when Edward married in 1999 and had children – Lady Louise in 2003 and the Viscount Severn in 2007. Andrew (and Sarah, Duchess of York) opted to have their daughters styled with all the trappings of their rank – the HRH and “Princess.” However, they will never work as full-time royals, so for all practical purposes they have one foot in the royal world and one foot out, which absolutely creates awkwardness.
Eugenie lives on the grounds of Kensington Palace and, as we saw a few days ago, can have a full-blown royal wedding with a tiara and a carriage ride through Windsor, but she doesn’t carry out engagements on behalf of her grandmother, and she won’t on behalf of her uncle or cousin later on. As she and Beatrice have worked to establish themselves as young professionals they’ve constantly run into side-eye and snark about how they’re using their position, their holidays, etc. Some of this is specific to the York family, but it’s a similar dynamic to what the Countess of Wessex faced back in 1999 and early 2000s when she attempted to maintain her career in PR after marrying Edward. It just wasn’t tenable, and while Beatrice and Eugenie are making it work, many would argue that they would have been better served had their parents eschewed equipping them with the weight of their titles.
Edward and Sophie have pointedly chosen a different path for their children, Louise and James. Still children, it remains to be seen how this truly plays out as they reach adulthood, but they have mostly flown below the radar and are treated akin to how their non-royal cousins, Peter Phillips and Zara Tindall, are – some interest, yes, but of a different, more benign sort to what Beatrice and Eugenie face. But unlike Peter and Zara, Louise and James could hold the same rank as the York girls, which makes the contrast all the more interesting.
My guess is that William and Harry have watched all of this play out quite closely over the years and Harry, who famously weighed whether he wanted to step outside the royal fold altogether, will at the very least strongly consider not styling his own children princes and princesses when the day comes.
The x-factor here is the softer stuff – popularity and image. Harry is quite literally the most popular member of the Royal Family, generating more consistent affection and goodwill than Andrew and Edward ever did, even in their heyday. As such, and depending on what private conversations have gone on between Charles, William and Harry about the latter’s future career, it’s entirely possible that the Sussexes will go the York route, but I would be slightly surprised.
That’s all very convoluted, I know, unless you take a particular interest in this stuff – and frankly I get twisted up on it from time to time myself. Tl;dr? Harry and Meghan’s child will not be prince or a princess as of his or her birth. That might change with the Queen’s intervention or when Charles ascends the throne, but the Sussexes may choose to skip the HRH stuff so that their children have an easier go of it making a living outside the Royal Family as adults.