Tyne and Wear Archives says that Northumberland Assize records are at the PRO
( Tyne and Wear archives has Newcastle quarter sessions records dating back to 1553,.Durham archives has QS back to 1596 ).
Unfortunately, the entry for the Northumberland Assizes at the Nat. Archives has a starting date of 1605 https://discovery.nationalarchives.gov.uk/details/r/C1139
I found one entry in the Nat Archives Cat. for 1604; thats a list of recusants presented at the Northumberland assizes(that's held in the Somerset archives )
If any records do exist they are unlikely to be online.
( I couldn't find them in the Nat Archives catatalogue but you could contact them and ask)