Question for republicans here - who would you replace the monarchy if you could?
I'm not really a republican, or even particularly anti-royal; but I am anti-the monarchy having any special rights / privileges; so my answer may be different to others.
I'm not sure they need replacing, but they need massively reducing; and there's no better opportunity than right now.
Keep the royal family to just the descendants of the monarch (which is why it's got so bloated currently); no privileges, no exemptions from the laws that apply to everyone else (eg taxation), no crown lands, no ***les (and same goes for all hereditary ***les) etc etc.
Pay them a stipend from the public purse if you must, decreasing amounts for those further from the throne. Relegate them to ceremonial role only, a head under a crown, and something to print on the stamps and coinage.
I'd also be happy to completely dispose of the need for a royal family at all - have the house of commons, with a PM, and an elected house of Lords, Senate, whatever - with a leader of their own - 20 year terms for the HoL (rolling 5 yearly), no opportunity for re-election (I don't want them having to go populist in order to keep their jobs) and some powers to actually keep a check on the government of the day. Leader of the Senate (or whatever you end up calling it) can be the ceremonial head of state, whilst the PM wields more power.
Might as well keep the name "House of Lords" and name everyone in it a Lord/Lady - purely for the sake of tradition and pageantry. Allow each major trade/profession to elect from within to hold office there (sadly, including politicians), same for the big charities, and some direct votes from the public, likely for celebrities and sports figures.
None of the above is particularly thought out and worked through - for now, the tastk is to severely shrink the size of the royal family, and eliminate all of their privileges.