Answer of the question Do Saptarishi exist in today's time? says:
Saptarshis live for a period of Manvantara. So, they are alive now.
Srimad Bhagavatam 8.13.5 gives names of seven sages for Vaivasvara Manvantara:
कश्यपोऽत्रिर्वसिष्ठश्च विश्वामित्रोऽथ गौतमः| जमदग्निर्भरद्वाज इति सप्तर्षयः स्मृताः ॥ ८.१३.५ ॥
Kaśyapa, Atri, Vasiṣṭha, Viśvāmitra, Gautama, Jamadagni and Bharadvāja are known as the seven sages.
Now I have two questions:
I. Jamadagni was killed by Kartvirya Arjuna's sons (Haihayas/Yadavas), so how he is alive?
In olden days, Rama, the son of Jamadagni, in anger at the death of his father, slew with his battle axe the king of the Haihayas. (Source)
How great is the crime that they have committed, in slaying with their deadly shafts an old man like you, wholly occupied with pious cares, and engaging not in strife! Much have they to boast of to their fellows and their friends, that they have shamelessly slain a solitary hermit, incapable of contending in arms!' Thus lamenting, bitterly and repeatedly, Ráma performed his father's last obsequies, and lighted his funeral pile. He then made a vow that he would extirpate the whole Kshatriya race. (Source)
II. Who was in Saptarshis (for Vaivasvara Manvantara) instead of Viśvāmitra earlier?
Vishvamitra was a kshatriya king earlier. But when Vasishta destroys all the weapons employed by Viswamitra (including Pasupata and Brahmastra) with his Brahmadanda, Viswamitra uttered these word:
Shame Where is the might of a kshatriya? The energy of a brahmin is the real energy. The staff of Brahma has singly destroyed all my weapons. Now I have realised the reason. With clear mind and senses, I shall undertake intense penance which will earn me brahminhood. (Valmiki Ramayana 1.56.23/24)
And later he did intense penance and acquired the titles of Rajarshi (Valmiki Ramayana 1.57.5), Rishi (Valmiki Ramayana 1.63.2), Maharshi (Valmiki Ramayana 1.63.18) and Brahmarshi (Valmiki Ramayana 1.65.19).