I am on my phone now, but if your partners table has a partner_id then you can do something like:
SELECT
p.organization_name
, p.email
, (SELECT
count(*)
FROM
partner_application_stories) AS 'referrals'
, pas.partner_id
FROM
partners AS p
INNER JOIN // Returns only matching rows if you want all rows in the p.partner table use LEFT OUTER JOIN or all in right the RIGHT OUTER JOIN
partner_application_stories AS 'pas'
ON p.partner_id = pas.partner_id
GROUP BY pas.partner_id
I won’t be at a computer until tomorrow, but give this a try and see if it works for you.