After the Star Trek: The Next Generation episode "Darmok", does the Federation ever establish open relations with the Tamarians?
Non-canon sources are welcome.
If so, how do they establish a form of communication with them?
According to Memory Beta the Federation and the Children of Tama do establish relations. This is not canon.
The Federation encountered the Tamarians seven times prior to 2368, but were never able to break the language barrier. In that year, Tamarian Captain Dathon beamed himself and Starfleet Captain Jean-Luc Picard of the USS Enterprise-D to the surface of planet El-Adrel IV, in hopes that a shared conflict would lead to mutual understanding and friendship. During this encounter, it was determined that the Tamarians communicated exclusively through cultural metaphors. Though Dathon was killed on the planet, the contact marked the opening of communication between the two cultures. (TNG episode: "Darmok")
The progress made in relations with the Tamarians following this breakthrough was considered one of the noteworthy accomplishments of Federation President Jaresh-Inyo and his administration. (ST novel: Articles of the Federation)
Roxana Novac was a linguist assigned to the Federation's Tamarian liaison office, and did much work in understanding the Tamarians' language. (SCE eBook: War Stories, Book 1)
In 2381, the Tamarian Doctor Sharak was assigned to the USS Voyager as CMO for its return mission to the Delta Quadrant. (VOY novel: Unworthy)
Although the species was encountered a total of seven times in the hundred years after first contact, formal relations were unable to be established, due to the complexity and provincial nature of the Tamarian language – which was entirely composed of metaphors derived from their collective experience and mythology.