Ashcombe, L. (born 1964). Last ran 2021 Conservative Peers by-election (replacing 3 peers); he received 1 vote (of 36). Previously ran in 2019 Whole House by-election receiving 15 votes (of 259)
Biddulph, L. (born 1959). A perennial candidate as he is "happy to be called on to serve" always, often running in the by-elections where the Carter Convention suggests that he should not. If we ignore the recent Whole House by-election (where a Labour peer was expected to be returned), he has never gained more than 2 votes, often 0.
Camrose, V. (born 1970). Succeeded to his title in 2016, and this is his first by-election as Colin mentions.
De La Warr, E. (born 1948). A regular candidate in these by-elections. Last ran in 2021 Whole House by-election receiving 15 votes (of 237). Previously ran in 2021 Conservative Peers by-election (replacing 3 peers); he received 1 vote (of 36).
Dormer, L. (born 1960). Ran as a cross-bencher as recently as 2019, but ran in the 2021 Conservative peers by-election receiving 0 votes (of 36) and 2021 Whole House by-election receiving 5 votes (of 237).
Dudley, E. (born 1947). He succeeded to his title in 2013 and this is first by-election as Colin mentions
Limerick, E. (Foxford, L.) (born 1963). A regular candidate in these by-elections. Last ran in 2021 in Whole House by-election receiving 12 votes (of 237). Previously ran 2021 Conservative Peers by-election (replacing 3 peers); he received 0 votes (of 36).
Monckton of Brenchley, V (born 1952). He succeeded to his title in 2006. A new candidate as Colin mentioned. He has been a bit of disruptor historically having previously regarded the House of Lords Act as unconstitutional and continuing to persist with claims that he was a member, eventually receiving a "cease and desist" letter from the House. I won't even get started on his public policy views.
Strathcarron, L. (born 1949) - Runner-up in the 2021 Whole House by-election receiving 46 votes (of 237). Previously ran 2021 Conservative Peers by-election (replacing 3 peers); he received 1 vote (of 36).
Windlesham, L. (born 1968) - A regular candidate in these by-elections. Last ran in 2021 in Whole House by-election receiving 10 votes (of 237). Previously ran 2021 Conservative Peers by-election (replacing 3 peers); he received 1 vote (of 36).
Notable by their absence:
Abergavenny, M. (born 1955). Has run in all Conservative Peer by-elections (though not all the relevant Whole House by-elections) since at least 2010.
Lord Strathcarron is my tentative favourite as the runner-up in a previous by-election, but this is a smaller electorate, so things might change. Ashcombe, Limerick and Windlesham have all put in performances that show some support in the House, and their age is probably favourable for them. Viscount Camrose as a new candidate and the youngest in the field could be a wildcard. De La Warr has shown some support in the past, but I think is now too old if he has not achieved election in several previous attempts. With another Conservative Peers by-election in the off-ing (anticipated retirement of Lord Rotherwick), a strong performance in this election may be indicative for the future.