Apenas a resposta postada para fechar a pergunta:
-- Set "1" for counting to be used later
WITH DATA AS (
SELECT
orders.id,
orders.client_id,
orders.deliver_on,
COUNT(1) -- Creates a column of "1" for counting the occurrences
FROM orders
GROUP BY 1
ORDER BY deliver_on, client_id
)
SELECT
id,
client_id,
deliver_on,
SUM(COUNT) OVER (PARTITION BY client_id
ORDER BY client_id, deliver_on
ROWS BETWEEN UNBOUNDED PRECEDING AND CURRENT ROW) -- Counts the sequential client_ids based on the number of times they appear
FROM DATA
