I think you need to quote the word high in the WHERE
clause. Single quotes are fine in Access SQL statements.
HighPriority = "UPDATE tblsearchengine01" & vbCrLf & _
"SET Query04priorityselect = 'xx' WHERE Priority <> 'high'"
Debug.Print HighPriority
CurrentDb.Execute HighPriority
If the query still throws an error, go to the Immediate window and copy the statement text which was output from Debug.Print
. You can then create a new query in the Access query designer, switch it to SQL View, paste in the copied text and test that statement. Hopefully you can figure out how to fix the error. If not, copy the statement text and include it in your question.