Adding a new record to the beginning of the approval chain from the delegation chain
My suggestion is to create a "RowID" computed column on the workflow.delegation_engine table.

ALTER TABLE workflow.delegation_engine ADD [RowID] AS
    cast(de.ApprovalOrder + 1 as varchar(4))
    + cast(de.EntityCode as varchar(8))
    + cast(de.DelegationCode as varchar(12))


Your comment indicates that you might be ordering the query on this column.  In that case, you might also want to apply an index on this column.  I haven't tried this out, so I don't know for sure whether an index on this column is allowed, but I think it does satisfy all of the requirements.

Also, you might want/need to pad your values with leading zeros in order to ensure that your calculated RowID is unique.  In that case, you might want to try the following:

    right('0000' + cast(de.ApprovalOrder + 1 as varchar(4)), 4)
    + right('00000000' + cast(de.EntityCode as varchar(8), 8)
    + right('000000000000' + cast(de.DelegationCode as varchar(12), 12)


This would provide uniqueness and would preserve ordering (i.e. ApprovalOrder 10 comes after ApprovalOrder 2).  If you don't care about ordering, then you might not need the leading zeros; you could just insert delimiters to ensure uniqueness.

    cast(de.ApprovalOrder + 1 as varchar(4))
    + '|' + cast(de.EntityCode as varchar(8))
    + '|' + cast(de.DelegationCode as varchar(12))


This would protect against a scenario where one row has ApprovalOrder: 1, EntityCode: 'ABC', DelegationCode: 'DEF' and another row has ApprovalOrder: 1, EntityCode: 'AB', DelegationCode: 'CDEF'.  In that case, the RowID for both rows would be '2ABCDEF'.  Adding the delimiters ensures that the first row would have RowID: '2|ABC|DEF' and the second row would have RowID: '2|AB|CDEF'.


Alternatively, if you can't or don't want to put a "RowID" computed column on the table, then you should be able to just structure the query as shown below.  Note that I've included an "order by" clause that was left out of the original query.  Comments indicate that the reason for the subquery in the original query was to order by the "RowID" column.  The order by 1 clause in the query below accomplishes the same result.

select
    cast(de.ApprovalOrder + 1 as varchar(4))
        + cast(de.EntityCode as varchar(8))
        + cast(de.DelegationCode as varchar(12)) as 'RowID' ,
    cast(de.ApprovalOrder as int) + 1 as 'ApprovalOrder' ,
    de.EntityCode ,
    de.CostCentre ,
    de.DelegationCode ,
    de.ProjectCode ,
    de.RoleGroup ,
    de.Position ,
    de.DelegationText ,
    de.DelegationAmount ,
    de.Active 
from
    workflow.delegation_engine de
where       
    de.EntityCode = @entity
    and de.ProjectCode = @project_code
    and de.DelegationCode = @delegation_code
order by
    1