On 5 September 2024 the government introduced the House of Lords (Hereditary Peers) Bill - Parliamentary Bills - UK ParliamentSee also the Explanatory Notes (pdf)
The Bill seeks to implement a Labour Party manifesto commitment to remove 'the remaining connection between hereditary peerage and membership of the House of Lords; to abolish the jurisdiction of the House of Lords in relation to claims to hereditary peerages ..'
The majority of hereditary peers were excluded from the House of Lords by the House of Lords Act 1999 (legislation.gov.uk) but a compromise was reached and section 2 of that Act provided for 90 such peers to continue as members. In addition the Earl Marshal and Lord Great Chamberlain were excepted.
The Bill states
In modern times. claims to hereditary peerages are rare and the Bill will abolish the ancient jurisdiction of the House of Lords over such claims.
If any claims arise