Mīmāṃsā has had a “split personality” for roughly the past millennium: interpretations generally follow one of the two great teachers, Kumārila Bhaṭṭa or Prabhākara Miśra, and attack the other. The historical development of these “two systems” still needs a good deal of research—it must have happened for entirely different reasons than the various splits within Vedānta, which were strongly linked to institutions and religious movements—but for now we can look at just a single point where Mīmāṃsakas ancient and modern have projected some ideas about this history, and where we can possibly attain some clarity. That point is “the Old Prābhākaras” (jaratprābhākara-).
First, I have only ever seen jaratprābhākara-, and not jaratprabhākara-. This should therefore refer to the “Old Followers of Prabhākara” and not “The Old Prabhākara.” But Subrahmaṇyaśāstrī for some reason has taken the latter course, suggesting (in his introduction to the edition of the Prakaraṇapañcikā, p. 24) that Old Prabhākara was a predecessor and teacher of Prabhākara, the author of the Bṛhatī.
Second, I am not aware of any author earlier than Vācaspati Miśra (late 9th century) using this phrase. And Vācaspati distinguishes between “Old Prābhākaras” and “New Prābhākaras.” The latter refers (primarily if not exclusively) to Śālikanāthamiśra. The former seems to be some Mīmāṃsakas who had slightly different interpretations of Prabhākara’s ideas. Contrast the interpretations given of Prabhākara’s statement “obligation, which has the fact that something is to be done as its content, does not denote the fact that something is to be done” (kartavyatāviṣayo niyogo na kartavyatām āha) in Vācaspati’s Nyāyakaṇikā (p. 77 of Mahaprabhu Lal Goswami’s edition). Jayapurī Nārāyaṇa Bhaṭṭa also refers to the Old Prābhākaras in his commentary to Śālikanātha’s Prakaraṇapañcikā. Śālikanātha himself doesn’t refer to the Old Prābhākaras, or quote from any texts of theirs, and I am not always sure that the “others” in the Prakaraṇapañcikā that Nārāyaṇa Bhaṭṭa identifies as Old Prābhākaras are actually “Prābhākaras,” that is, followers and interpreters of Prabhākara Miśra. They don’t seem to follow Prābhākara particularly closely, and indeed Śālikanātha uses Prabhākara’s remarks to argue against them. They might possibly be older Mīmāṃsakas.
Third, this raises the issue of Śālikanātha’s proximity to Prabhākara. Later scholars, such as Vācaspati, clearly thought that Śālikanātha was several generations removed from Prabhākara. More recent authors have been misled into thinking that Śālikanātha was Prabhākara’s student by Śālikanātha’s commitment to defending and explicating the thought of the person he calls his guru. What would be useful to know is whether Śālikanātha ever refers to other people in his interpretations of Prabhākara’s comments. As it stands, it appears as if a few groups of scholars were studying Mīmāṃsā through Prabhākara’s commentary independently, and later on Vācaspati distinguished these groups as Old and New Prābhākaras.