You could either use that query as a subquery:
) AS subquery
WHERE subquery.alan > [some_value]
or you have to add a column and populate it in your table via any DB client (I don't know how Carto let's you access one of their hosted DBs. Or do you host your DB yourself?)
EDIT: It seems like you can query the DB to alter the data structure just as normal via SQL. In that case you can add and populate a new column like so:
ALTER TABLE pl_park ADD COLUMN area numeric;
UPDATE pl_park SET area = ST_Area(pl_park.the_geom::geography);
Not-asked-for-advice: it´s not always best practice to simply add arbitrary calculated data as new columns to your DB tables. You can use views or prepared queries to quickly get calculated values from your tables.
In this case, though...why not.