How to trigger AFTER UPDATE in Postgres

I'm trying to run a procedure/function when a table gets updated (insert/delete/update), however, the function doesn't appear to get run when the trigger occurs or the trigger doesn't get triggered on an insert.

Function and Trigger:

CREATE OR REPLACE FUNCTION fn_rental_trigger() RETURNS TRIGGER AS $$
   BEGIN
    CALL get_top_ten_rentals();
    RETURN NULL;
   END; $$
LANGUAGE plpgsql;

CREATE TRIGGER tr_new_rentals
    AFTER UPDATE ON public.rental
    EXECUTE FUNCTION public.fn_rental_trigger();

insert call:

INSERT INTO public.rental (rental_date, inventory_id, customer_id, return_date, staff_id, last_update)
VALUES (NOW(), 4030, 459, NOW() + interval '7 day', 1, NOW());

The stored procedure works as expected, and when I run it solo I get what I want. Running it from a trigger is failing with every way I attempt, so what's the correct way to run a trigger that executes a working procedure on a table update?

For context, this is based off of the dvd rental database from the postgres tutorial website.

Edit

stored procedure:

CREATE OR REPLACE PROCEDURE get_top_ten_rentals()

AS
$$

-- Start a tansaction to get the data
BEGIN
    
    -- clear out existing data to refresh list
    DELETE FROM report.top_ten_rentals;

    INSERT INTO report.top_ten_rentals (title, inventory_id, rating, length, times_rented, total)
    SELECT f.title AS title,
           r.inventory_id AS inventory_id,
           f.rating,
           fn_transform_length(f.length),
           COUNT(*) AS times_rented,
           SUM(p.amount) AS total
    FROM public.payment AS p
        JOIN public.rental AS r ON p.rental_id = r.rental_id
        JOIN public.inventory AS i ON r.inventory_id = i.inventory_id
        JOIN public.film AS f ON i.film_id = f.film_id
    GROUP BY r.inventory_id, f.title, f.rating, f.length
    ORDER BY total DESC
    LIMIT 10;

    -- Rollback when there is an exception to preserve data integrity
    EXCEPTION
        WHEN OTHERS THEN
            ROLLBACK;
END;
$$

LANGUAGE plpgsql;

To answer Adrian Klaver's other questions:

• Yes, and that's intentional but open to change.
• Because it is a requirement, a silly one, but still required.

I have also attempted to run the trigger as so:

CREATE TRIGGER tr_new_rentals
    AFTER UPDATE ON public.rental
    FOR EACH ROW
      EXECUTE FUNCTION public.fn_rental_trigger();

In case running per row was needed, however, that also does not execute the procedure so the table I'm trying to update never receives any data.