Picture of letter here: https://www.reddit.com/r/mildlyinteresting/comments/b1fikk/a_letter_from_one_of_my_relatives_in_1836_written/
"Europe. Rome. 30th Decr /36 Dear Father I hope you will receive my letter last week announcing my safe arrival here after sundry adventures &c &c. Since then I hardly know how to relate events. I got here late Sunday 18th, next morning called on the French Embassador for whom I had letters, gloves &c from De Neve (?) - after passing rooms the size and splendour of which made me shiver I reached his Excellency, a tall gaunt kingly Marquis, who received me in Royal style &c &c and after his returning "mille remerciments" I was with equal dignity walked out - Tolassia (?) came next - he was very civil & after some consideration gave me an introduction to the Hanoverian Embassador Le Chevalier Kestsier (?) - called on him & after long chat he promised to try his utmost - make interest &c &c &c and let me know & to my delight obtained permission & the 23 at 11 o'clock was fixed 'sash' (?) - he told me I must address the Pope in Italian or French - heigh ho! - be in full dress - well the day arrived & an hour before the time you might have seen me the Petition in one hand - Chapeau hat (?) in the other - figuring away before the glass - to a minute the Embassador came in his state carriage with 3 state servants //// off he drove I following in my own carriage & state monkey of an Italian behind - umph - Lord Stewart & servants in another, but to shorten this adventure, I was presented & you will smile perhaps when I say I acquitted myself famously - his Holiness received me in the kindest & most gracious manner giving me his blessing, thanking me for the care & trouble I had taken of the letter (I think he fancied I brought it from India) – I spoke to him in French – my address I had written previously & learnt by heart – that over – I was then put to my trumps – however I was with him ¼ of an hour nearly or quite & ventured to urge the request in the strongest at the same time humblest terms. I have written all this to Cockburn (?) to end this subject – I have obtained no reply & his Holiness seems disposed to take some time to consider of it – as it involves an important Political question – I shall wait no longer – as it is I fear I have remained too long – my great wish being to reach Gloucester the 3 or 4 Feby – the Boardmeeting on the 5th – I fear this will be impossible. I therefore write to Skey (?) guarding (?) this point & as I at the same time send part to Minny (?) you need not forward this unless a convenient Frank."
The letter continues but this is the relevant part.
This answer is speculative, of course, but it is possible that the letter refers to the split among the Anglican communion, between 'high church' Anglo-Catholics and 'low church' evangelicals; the latter tending to tolerate Dissenters, e.g. Methodists.
In the aftermath of the Catholic Relief Act of 1829 (i.e. legal emancipation of Catholics), the question of toleration became a pressing topic. The 'London University' established in 1826 to grant higher education to non-Anglicans, including Catholics and Jews (who were barred from Oxford and Cambridge), was finally granted its royal charter in 1836. It became present-day University College London, whereas King's College London was established specifically as an institution for Anglicans. Also in 1836, the appointment of Renn Hampden, a liberal cleric who tolerated Dissenters, to the Regius Professorship of Divinity at Oxford, sparked further controversy over the privileges granted to Anglicans. The opposition to this appointment by 'Tractarians', or high-church Oxford clerics, was one of the catalysts for the establishment of Anglo-Catholic Oxford Movement.
So it is plausible, given the date, and the fact that your ancestor seems to have been acting in some kind of official diplomatic capacity, that the 'political question' being considered by the Pope was one concerning the relationship between the Anglican and the Roman Catholic churches. As the Pope in question would have been Gregory XVI, an ultramontane conservative, this would have been an issue of international relations, as much as one of religious belief.
EDITED TO ADD: the 'Political Question' might specifically refer to the Tithe Wars in Ireland. Irish Catholics were still required to pay tithes to the Anglican church, even after emancipation, and this resulted in various disturbances between 1831-36. The Tithe War was supported by the Roman Catholic church, and this pressure eventually resulted in the British government reducing the amount of tithes payable... could be that the letter concerns this issue?
So, it might be helpful to have a few more details. What country did your ancestor live in? Was he associated with any political movements or parties? What did he do for a living?
What's with the grid layout of the letter?