How I can insert a list of values into a new column of the already existing in PostgreSQL?

For example, I have some text values:

( 'apple', 'orange', 'banana' )

And I have a table:

I need, that my table looking like this:

How can I do this?

I found only solutions, that can fill New Column with only one default value, random values and sequences like (1,2,3,4,5), but it isn't what I looking for.

This is one approach that might satisfy your requirements:

UPDATE some_table
  SET column3 = new_values.column3
  FROM (SELECT column1,
               column2,
               ('{apple, orange, banana}'::text[])[row_number() OVER (ORDER BY column1, column2)] AS column3
          FROM some_table) new_values
  WHERE some_table.column1 = new_values.column1
    AND some_table.column2 = new_values.column2;

This approach can easily be modified to cycle through the new column values until all of some_table's rows have a value in the new column by doing the following:

WITH t(value_list) AS (
  VALUES ('{apple, orange, banana}'::text[]))
UPDATE some_table
  SET column3 = new_values.column3
  FROM (SELECT column1,
               column2,
               t.value_list[(row_number() OVER (ORDER BY column1, column2) - 1) % array_length(t.value_list, 1) + 1] AS column3
          FROM some_table CROSS JOIN t) new_values
  WHERE some_table.column1 = new_values.column1
    AND some_table.column2 = new_values.column2;