I know of many long-running series that, in their later seasons, would add younger children to the cast since the original children were now teens or college age. These are the ones I know of:
My Three Sons--Ernie
The Brady Bunch--Oliver (definitely the most infamous and best-known of the added children)
Here Come the Brides--Molly and Christopher
Little House on the Prairie--James and Cassandra
The Waltons--Jeffrey and Serena
Are there any others?
This phenomenon is not limited to TV shows. I know of one book series, written in the early 1900s (about the time TV was being invented), and that is Anne of Green Gables. In the later books, after Anne was a teenager, Lucy Maud Montgomery added Davy and Dora to live with Marilla.