Alistair Brown, Art UK added: ‘One other online comment suggests this could be Lady Mary Wroth - based on what appears to be an original inscription https://bit.ly/3xsDJQ1’

You may well be right. The inscription claiming that this is Aletheia, countess of Arundel in 1605 is certainly suspect. It is not in a contemporary hand, and Aletheia did not marry Thomas Howard, earl of Arundel until the summer of 1606.

I personally am rather more interested in who painted this highly accomplished portrait. One possibility is Daniel Mytens, whose first important patron in London was Thomas Howard, Earl of Arundel. His known portrait (c. 1618) of Alathea, Countess of Arundel, is below:

https://bit.ly/3hvRHLa

Other possibilities include Paul van Somer, William Larkin and, less likely, Cornelius Johnson.

Robert Peake has also been suggested as the potential artist here, but while that is not out of the question, I find him less likely.

Unless Lady Mary (Sidney) Wroth was a Catholic, would she have worn an IHS jewel as in this picture?

Paul van Somer the most likely artist of those suggested. Not Larkin, Johnson or Peake.

The known portraits of the Countess of Arundel by Mytens and Rubens do not look like our sitter, whose face is more striking. Those known portraits show a rather bland, placid face.

Jacob, what do you think about Mytens?

The portrait lacks Mytens' solidity.

It is a tricky one. Attached is a composite between our portrait and one by Van Somer on ArtUK, a full-length described as Portrait of an Unknown Lady, Paulus van Somer I (1576–1621) (style of), National Trust, Penrhyn Castle.

Except that I have taken a detail from the full-length and reversed it.

I think that our portrait is a fragment of a larger picture. Arms were never cut off in this crude way in portrait of the period. I think that the Aetat 32 – 1619 is a copy of the original inscription.

Our portrait is by or after Van Somer, I suspect.

Yes, Jacob, that is very suggestive, assuming the Penrhyn picture has been properly attributed. Interestingly, according to the NT entry, it was previously attributed to Mytens, and is now listed as "manner of Paulus van Somer" and dated c. 1615-1620. Another picture at Penrhyn, also listed as manner of van Somer and also previously attributed to Mytens, is below:

https://bit.ly/3yILWQo

To my eye, if this is by van Somer, the face is above his usual level. It is a rather intense face, which would appear to go rather better with a woman like Mary Sidney/Wroth than the Countess of Arundel, but that is hardly proof.

I discussed this portrait with my former PhD student Chris Higgins back in 2016. The current identification to Aletheia, countess of Arundel, is unsustainable, but as Ingestre Hall later became a Talbot property, the sitter may nonetheless be a Talbot lady. Looking for one such, qualified as possibly ‘Aetat 32/ 1619’, there is the relatively overlooked first cousin of the celebrated three Talbot sister-countesses: Gertrude (b. circa 1588), da. of Henry, younger bro of Gilbert and Edward, 7th and 8th earls of Shrewsbury. She married Robert Pierrepoint, later 1st earl of Kingston upon Hull. The Pierrepoints were fervently Catholic, which accords with the IHS jewel. There are few known records of Gertrude, though the diarist of Ben Jonson's walk to Scotland notes her at Welbeck when Jonson dined there, referring to her as ‘Mrs Purpoint’, possibly not a Jac spelling variation but a pun, particularly if Gertrude had a reputation as a fancy dresser, a purpoint being a high-fashion quilted doublet (N.B., Mary Q of S, described at her execution: 'Her purpoint was of black figured satin'). Chris, at the time, drew my attention to its likeness to the sitter in the Penrhyn portrait, which is indeed persuasive. By/after Van Somer.

Please take a look at the attached portrait of Sir Philip Sidney, Lady Wroth's uncle. I find the resemblance striking.

This discussion, “Could this actually be a portrait of Lady Mary Wroth?”, asks about the identity of the sitter but inevitably questions around the artist have also risen.

On the artist, by or attributed to Paul van Somer is favoured in my post of 9 July, Jacinto’s of 10 July and Tim Wilks of 12 July. While I think the portrait is probably autograph, it is difficult to be confident from a web image so I would suggest “Attributed to Paul van Somer”.

On the sitter, this is more difficult. I think we can rule out Lady Mary Wroth who may be the right age but without other supporting evidence. The inscription on the portrait identifying it as Alathea Talbot, Countess of Arundel and Surrey, is clearly not original and this identification is not tenable.

Tim has tentatively asked if the portrait could represent Gertrude Talbot (b. circa 1588), who married Robert Pierrepoint, later 1st earl of Kingston upon Hull. The same objection arises as for Lady Mary Wroth, i.e. Gertrude Talbot may be the right age but we do have much other supporting evidence. I think it will be difficult to take matters of identification further.

So my sense is that the title should be changed to Unknown lady, called Alathea Talbot (c.1590–1654), Countess of Arundel and Surrey, and the artist to Attributed to Paul van Somer. Or something along these lines.

I fully expect it's autograph work, and if by van Somer, then a quite fine example of his work.

If it is Gertrude Pierrepont then this is the husband
https://www.easyliveauction.com/catalogue/lot/4d0fba8061aa349b2ff6d670175b228e/0af8d24542e81eb9357e7ef448a6646f/the-winter-fine-art-old-masters-antiques-and-antiquarian/
who looks a lot like
https://www.artandthecountryhouse.com/catalogues/catalogues-index/called-sir-roger-townshend-kt-15441590

Looking at the dress- this is someone of the highest status-possibly royal.
Here is Elisabeth of France with similar dress.
https://www.meisterdrucke.ie/fine-art-prints/Unbekannt/726908/Portrait-of-Elisabeth-of-France-1602-1644,-Queen-consort-of-Spain,-c.-1620.html
On a look alike basis- here is a very similar portrait facewise of Lady Anne Clifford by Larkin
https://www.npg.org.uk/collections/search/portrait/mw235435/Anne-Countess-of-Pembroke-Lady-Anne-Clifford

This remarkable portrait should be addressed by a Jacobean period specialist. What does Group Leader Rab MacGibbon think of it?