Subtract one month from the current month, then “truncate” that to the beginning of that date. As you don’t want to include rows from “this” month, you also need to add a condition for that
SELECT *
FROM Conference
WHERE date_start >= date_trunc('month', current_date - interval '1' month)
and date_start < date_trunc('month', current_date)
date_trunc('month', current_date - interval '1' month) will return the 1st day of the previous month and date_trunc('month', current_date) will return the first day of “this” month.