Prime was only suppressed for the Roman cathedral office. It was not suppressed for any of the other Latin offices.
From Sacrosanctum Concilium:
d) The hour of Prime is to be suppressed.
It has been suppressed, for the Liturgy of the Hours. Of course Summorum Pontificum has allowed the 1960 Breviary to be used; initially when the LOTH was proclaimed, the old breviary was only to be allowed for the use of elderly clergy for whom learning a new breviary was an obstacle:
For those however who, because of advanced age or for special reasons, experience serious difficulties in observing this new Order, it is lawful to continue to use the former Roman Breviary, in whole or in part, with the consent of their Ordinary, but only when reciting the Office alone.
(Paul VI decree on the LOTH of the Hours “Laudis Canticum”)
In the post-Vatican II Monastic Offices, only schema A, the traditional Benedictine psalter, allows for the retention of Prime
ad libitum (the other schemas make no allowance for Prime). Most monasteries have abolished it, and have redistributed the psalms of Prime to other hours. It makes practical sense: monastic Matins is very long (12 psalms and two long readings, plus a third nocturne on Sundays, feasts and solemnities), followed by Lauds then Prime. Monasteries have instead elected to allow more time between Matins and Lauds to allow for private lectio divina.
Indeed Lauds traditionally is the dawn office; normally it followed very shortly after Matins (the Rule of Saint Benedict states a short interval between the two to allow for taking care of “natural needs”, i.e. a bathroom break…). In early monastic times, the monastic day was very elastic and followed the sun, so that Matins had to be shortened in summer to ensure Lauds still occurred at daybreak. Now the practice is fix the time of the offices according to the clock regardless of season, and Lauds has evolved to take the hinge place in the morning, crowding out Prime. A longer gap between Matins and Lauds is now where most abbeys allow time for private lectio, and after Lauds, usually the monks begin their daily work, pausing for Mass and the other offices; since there are no longer choir monks and lay brothers to do the physical work (all monks having the same rank), all monks are bound to choir, and all monks participate in the daily work of the abbey (which was the original intent of St. Benedict).
It made sense to allow the old breviary to return to fuller use when SP allowed wider use of the EF Mass; the liturgical year and calendars are of course a better fit, and of course Prime is part of that Office, and remains part of the monastic breviary for those communities using the EF Mass, and those using the OF who have chosen to retain Prime.