Canon 686. §1 With the consent of the council, the supreme moderator for a grave cause can grant an indult of exclaustration to a member professed by perpetual vows, but not for more than five years, and if it concerns a cleric, with the prior consent of the ordinary of the place in which he must reside. To extend an indult or to grant it for more than five years is reserved to the Holy See, or to the diocesan bishop if it concerns institutes of diocesan right.
[revised wording according to m.p. Competentias quasdam decernere, 11.II.2022]

§2 Only the Apostolic See can grant an indult of exclaustration for cloistered nuns.

NB Congregation for Institutes of Consecrated life and Societies of Apostolic Life,
Instruction Cor Orans, 1 April 2018:

130. In exemption of can. 686, §2 CJC, the Federal Council gives its consent for the request of the indult of exclaustration for a nun of solemn vows, after the year granted by the Major Superior of the monastery, up to the completion of three years.
[Exemption approved by the Holy Father in a specific form.]

131. The Federal Council gives its consent for the request for the extension of the indult of exclaustration for a nun of solemn vows, to be requested from the Holy See.

[Exemption approved by the Holy Father in a specific form.]

177. In derogation of can. 686, §2 CJC, the Major Superior, with the consent of her
Council, can grant the indult of exclaustration to a nun professed with solemn vows, for not more than a year, after the consent of the Ordinary of the place where the nun will have to live, and after having heard the opinion of the diocesan Bishop or of the competent religious Ordinary.
[Exemption approved by the Holy Father in a specific form.]

178. In derogation of can. 686, §2 CJC, an extension of the indult of exclaustration can be granted by the Federal President with the consent of her Council, for a nun professed with solemn vows of a monastery of the Federation for a period of no more than two years.
[Exemption approved by the Holy Father in a specific form.]

§3 At the request of the supreme Moderator acting with the consent of his or her council, exclaustration can be imposed by the Holy See on a member of an institute of pontifical right, or by a diocesan Bishop on a member of an institute of diocesan right. In either case a grave reason is required, and equity and charity are to be observed.