@vbaghi said:
After adding tmdb logo
Hello,
I’d like to use the API on my website.
After adding the logo, do I need to submit a request for approval?
If so, where should I send the request?

It is not necessary.
Just follow the instructions on this page.
https://www.themoviedb.org/about/logos-attribution
And of course, do not make it as small as the letters on an insurance contract. :-)