If I'm reading the question right, you could use a combination of a few variables, a `cte`, and the `row_number()` function to write this type statement. You can add more conditions to the cte to get to the exact data set you are looking for, and drop the `TOP` variable if it isn't helpful.

e.g. rextester: http://rextester.com/OIBEDZ93140
updated: http://rextester.com/TGZR4250
    
    if exists (select * from tempdb.sys.objects where name like '#retailtransactiontable%') begin; drop table #retailtransactiontable; end;
    create table #retailtransactiontable (
        [store] [nvarchar](10) not null
      , [terminal] [nvarchar](10) not null
      , [type] [int] not null
      , [transactionid] [nvarchar](44) not null);
        
    insert into #retailtransactiontable (store, terminal, [type], transactionid) values
    ('1','2',1,'Store1-Terminal2-T1'), ('1','2',2,'Store1-Terminal2-1'), ('1','2',2,'Store1-Terminal2-13'), ('1','2',2,'Store1-Terminal2-5'), ('1','2',2,'Store1-Terminal2-7'), ('1','2',2,'Store1-Terminal2-9')
      
    select * from #retailtransactiontable;
    
    declare @FirstTransactionIdToUpdate int = 5;
    declare @NewTransactionIdStart      int = 2;
    
    with cte as (
       select 
            store
          , terminal
          , type
          , transactionid
          , transint = convert(int,(right(transactionid,charindex('-',reverse(transactionid))-1)))
          , newtransactionid = 'Store'+convert(nvarchar(10),Store)
                             + '-Terminal'+convert(nvarchar(22),Terminal)
                             +'-'+convert(nvarchar(3)
                                ,((@NewTransactionIdStart+(row_number() over (order by transactionid))-1)))
          --, newid = (@NewTransactionIdStart+(row_number() over (order by transactionid))-1)
          from #retailtransactiontable
          where store='1'
            and terminal='2'
            and [type]=2
            and convert(int,(right(transactionid,charindex('-',reverse(transactionid))-1))) >= @FirstTransactionIdToUpdate
        )
        --select * from cte
        update cte set transactionid = newtransactionid;
    
    select * from #retailtransactiontable;
    
before:
    
    store      terminal   type        transactionid
    ---------- ---------- ----------- --------------------------------------------
    1          2          1           Store1-Terminal2-T1
    1          2          2           Store1-Terminal2-1
    1          2          2           Store1-Terminal2-13
    1          2          2           Store1-Terminal2-5
    1          2          2           Store1-Terminal2-7
    1          2          2           Store1-Terminal2-9
    
after:
    
    store      terminal   type        transactionid
    ---------- ---------- ----------- --------------------------------------------
    1          2          1           Store1-Terminal2-T1
    1          2          2           Store1-Terminal2-1
    1          2          2           Store1-Terminal2-2
    1          2          2           Store1-Terminal2-3
    1          2          2           Store1-Terminal2-4
    1          2          2           Store1-Terminal2-5