My Language Exchange has been growing since 2000. Although the website seems out of date, it still has an active community of millions of language-learners who speak almost 200 native languages (including less commonly studied languages).
You can choose a pen pal by reading their bios, or there is a chat room available for you to instantly connect with a language exchange partner — note that if you create a Gold account, you can initiate chats with other users, but as a regular user, you will have to wait to be contacted.
Using the Cormier Method, the website provides tools to help intermediate speakers effectively practice with other learners. It advertises a Chat Companion with lesson plans to accompany your exchange, or lesson plans developed by teachers (although the quality of these resources varies drastically).
You can also find language teachers on the site, but given that the transactions take place directly between you and the teacher, you may feel safer using a 3rd party platform like italki or Verbling.
Although there are outlines on how to participate in language exchanges, how these outlines are followed depends entirely on you and your partner(s). My Language Exchange will help you build connections with other learners, but it’s up to you to plan how to practice. The concepts can also be used with any language exchange platform, such as Lingbe, italki, Tandem, and Amikumu.