Convert to CTE or Window function or a set or a merge statement
Without knowing your RDBMS, and with the very vague description you're giving, here's my initial approach.

It's basically taking your Subquery and converting it to CTE.

I'd suggest a more elaborate WHERE clause on that CTE, as right now it returns All rows from that table (which can take a while depending on how much data you have).

Things get a bit hairy, as you're inner joining a table to itself, and using that join to update THAT same table.  I'd tread very lightly and ensure you have a good test environment.

Maybe converting "a" to CTE is a better approach than converting "b" to CTE (since "a" actually has a WHERE clause).  Or maybe having BOTH of them as CTE is an even better approach to simplify the UPDATE.

;WITH CTE_tblsname_KS
AS
(SELECT linked_pmt_id
      ,pmt_id
      ,prop_name
      ,prop_addr1
      ,prop_city
FROM tblname_KS (NOLOCK)
)

UPDATE a
SET a.linked_pmt_id = b.linked_pmt_id
  , a.looptag = '1Mb-NBCBZ'
FROM tblname_KS a 
INNER JOIN CTE_tblsname_KS b
ON ISNULL(a.prop_name,'NULL') = ISNULL(b.prop_name,'NULL') AND 
   ISNULL(a.prop_addr1,'NULL') = ISNULL(b.prop_addr1,'NULL') AND 
   a.prop_city = b.prop_city
WHERE   a.linked_pmt_id IS NULL AND
    (a.status &lt;&gt; 'U' AND  a.addr_type NOT IN ('GIS LOCATION','ASSIGNED LOCATION') AND a.addr_type IS NOT NULL) AND
    a.prop_city IS NOT NULL AND
    a.prop_zip IS NULL