Canon 312. §1 The authority which is competent to establish public associations is:

1° the Holy See, for universal and international associations

2° the Episcopal Conference in its own territory, for national associations which by their very establishment are intended for work throughout the whole nation;

3° the diocesan Bishop, each in his own territory, but not the diocesan Administrator, for diocesan associations, with the exception, however, of associations the right to whose establishment is reserved to others by apostolic privilege.
[NB see Rescript “ex audientia Ss.mi” of 15 June 2022 requiring the diocesan bishop, before erecting – by decree – a public association of the faithful with a view to becoming an institute of consecrated life or a society of apostolic life, to obtain the written permission of the Dicastery of Consecrated Life and Societies of Apostolic
Life: cf. can. 579]

§2 The written consent of the diocesan Bishop is required for the valid establishment of an association or branch of an association in the diocese even though it is done in virtue of an apostolic privilege. Permission, however, which is given by the diocesan Bishop for the foundation of a house of a religious institute, is valid also for the establishment in the same house, or in a church attached to it, of an association which is proper to that institute.