How do I add a where statement at the end of query for a column that does not have a table to reference from?
Use the WITH clause to get the result set and SELECT only the wanted rows.
WITH CTE As (
select
CASE WHEN (to_char(((case when v.trip_order_start_date is null then case when v.manual_start_date is null then t.required_pickup_date else v.trip_order_start_date end else v.trip_order_start_date end  + (interval  '-1 hours' * ofc.offset)) at time zone 'utc' at time zone 'America/Chicago' + (interval  '-1 hours' * ofc.offset)) at time zone 'utc' at time zone 'America/Chicago', 'YYYYMM') &lt; to_char((now() at time zone 'utc' at time zone 'America/Chicago'), 'YYYYMM')
        AND(coalesce(posted_date, paid_date) IS NULL
            OR to_char((coalesce(v.posted_date, v.paid_date) + (interval  '-1 hours' * ofc.offset)) at time zone 'utc' at time zone 'America/Chicago', 'YYYYMM') &gt; to_char((now() at time zone 'utc' at time zone 'America/Chicago' - interval '1' month), 'YYYYMM'))) THEN 'YES' ELSE 'NO' END AS accrual
) 
SELECT * FROM CTE WHERE accrual = 'YES'

Or use the SELECT query as SUBSECT in a FROM clause and use that
SELECT * FROM (
    select
    CASE WHEN (to_char(((case when v.trip_order_start_date is null then case when v.manual_start_date is null then t.required_pickup_date else v.trip_order_start_date end else v.trip_order_start_date end  + (interval  '-1 hours' * ofc.offset)) at time zone 'utc' at time zone 'America/Chicago' + (interval  '-1 hours' * ofc.offset)) at time zone 'utc' at time zone 'America/Chicago', 'YYYYMM') &lt; to_char((now() at time zone 'utc' at time zone 'America/Chicago'), 'YYYYMM')
            AND(coalesce(posted_date, paid_date) IS NULL
                OR to_char((coalesce(v.posted_date, v.paid_date) + (interval  '-1 hours' * ofc.offset)) at time zone 'utc' at time zone 'America/Chicago', 'YYYYMM') &gt; to_char((now() at time zone 'utc' at time zone 'America/Chicago' - interval '1' month), 'YYYYMM'))) THEN 'YES' ELSE 'NO' END AS accrual
    ) t1 
WHERE accrual = 'YES'

In both cases you need a valid SELECT