While there are four vacancies in the order,only three of them are likely to be filled on 23 April as Sir Thomas Dunne only died in January and it takes the Palace about a year to decide on a replacement(one of the vacancies was caused by the death of Lord Boyce who died in November 2022).
Note that the order contains only 4 hereditary peers:Abercorn,Salisbury,Brookeborough & Shuttleworth.There are 12 life peers and 4 knights or ladies who hold no other title.
14 holders owe their appointment to political or government service,which I think is unbalanced.5 are lord lieutenants.There are 2 military members which is over representation given the country is not at war and the number of service personnel is at a record low.Lord Lloyd Webber is the only holder who does not owe his appointment to government service or service to the Crown.
It is rare now for a knight appointed to be under 70-to do otherwise means the membership will be clogged.Acccordingly the former PM's will have to wait-and some of them may never be honoured(LIz Truss springs to mind due to the shortage of her tenure).
As to Gordon Brown,I suspect he has been offered and refused both the garter and the thistle.As SS notes,there are no thistle vacancies at the moment.