Gaga and Azealia wrote 2 songs, 'Ratchet' and 'Red Flame.' However, Azealia is only featuring on 'Red Flame' and Gaga said that she was looking for a female vocalist to feautre on 'Ratchet' about 4 months ago. A lot of people are speculating about whether the two will collaborate after they both posted these pics on Instagram recently.
Gaga also said that the continuation of 'Telephone' was on ARTPOP, and that she wouldn't do it without Beyoncé, so maybe this is the continuation of the Paparazzi/Telephone trilogy.