Since your question is more focused on Lord Hanuman let me mention about him first - Shrimad Bhagvat Puran Canto 5 Chapter 19 states that he lives in the Kimpurush Varsha listening to Ramayan being sung by the denizens of the place and himself joining them in
किंपुरुषे वर्षे भगवन्तमादिपुरुषं
लक्ष्मणाग्रजं सीताभिरामं रामं तच्चरणसंनिकर्षाभिरतः परमभागवतो- हनुमान् सह किंपुरुषैः
आर्ष्टिषेणेन सह गन्दर्वैरनुगीयमानं
परमकल्याणीं भर्तृभगवत्कथां समुपशृणोति स्वयं चेदं गायति ॥
S'rî S'uka said: 'In the land of Kimpurusha the supreme and greatest devotee Hanumân delighting in service at His feet is together with the people always engaged there in worship of the Supreme Lord Râmacandra, the Original Personality who as the elder brother of Lakshmana is so
pleasing to Sîtâ.
Together with Ârshthishena [the leader of Kimpurusha] attentively listening to the stories about his most auspicious master and Lordship being chanted by a company of Gandharvas, he Hanumân himself prays thus.
The reference about Lord Parshurama has already been given so I won't repeat the same. The Kathasaritsagar mentions the story of a man named Lohajangha reaching Lanka in a flood where the Rakshasas take him to Vibhishan. This story is from a time period after Mahabharat since it mentions Mathura as the city of Krishna:
And finding that he was on the other side of the sea, he was astonished, and looked upon the whole thing as a daydream; then he saw there to his terror two horrible Rākṣasas, and those two for their part contemplated him from a distance with feelings of fear. Remembering how they were defeated by Rāma, and seeing that Lohajaṅgha was also a man who had crossed the sea, they were once more alarmed in their hearts. So, after they had deliberated together, one of them went off immediately and told the whole occurrence to King Vibhīṣaṇa.
King Vibhīṣaṇa, too, as he had seen the prowess of Rāma, being terrified at the arrival of a man, said to that Rākṣasa: “Go, my good friend, and tell that man from me, in a friendly manner, that he is to do me the favour of coming to my palace.”
The Rākṣasa said, “I will do so,” and timidly approached Lohajaṅgha, and told him that request of his sovereign’s. Lohajaṅgha for his part accepted that invitation with unruffled calm, and went to Laṅkā with that Rākṣasa as his companion. And when he arrived in Laṅkā he was astonished at beholding numerous splendid edifices of gold, and entering the king’s palace he saw Vibhīṣaṇa.
Kripacharya is also mentioned in the Mahaprasthanika Parva of Mahabharat to have become the guru of Parikshit so he was there at least in the beginning of Kaliyug:
"Having said these words, king Yudhishthira the just, along with his brothers, promptly offered oblations of water unto Vasudeva of great intelligence, as also unto his old maternal uncle and Rama and others. He then duly performed the Sraddhas of all those deceased kinsmen of his. The king, in honour of Hari and naming him repeatedly, fed the Island-born Vyasa, and Narada, and Markandeya possessed of wealth of penances, and Yajnavalkya of Bharadwaja’s race, with many delicious viands. In honour of Krishna, he also gave away many jewels and gems, and robes and clothes, and villages, and horses and cars, and female slaves by hundreds and thousands unto foremost of Brahmanas. Summoning the citizens, Kripa was installed as the preceptor and Parikshit was made over to him as his disciple, O chief of Bharata’s race.
Others are supposed to appear in the future but not sure if they would appear or show some signs of their existence in the Kaliyug itself. For example, Ashwatthama is supposed to become the next Vyas according to the Vishnu Purana:
These are the twenty-eight elder Vyásas, by whom, in the preceding Dwápara ages, the Veda has been divided into four. In the next Dwápara, Drauńi (the son of Drońa) will be the Vyása, when my son, the Muni Krishńa Dwaipáyana, who is the actual Vyása, shall cease to be (in that character).
Similarly, as mentioned in this chapter of the same Purana, he shal also be one of the Saptarishis and Maharaj Bali shall become the next Indra but all that is in the next Manvantar:
The son of Chháyá, who was called also a Manu, was denominated Sávarńi 6, from being of the same caste (Savarńa) as his elder brother, the Manu Vaivaswata. He presides over the ensuing or eighth Manwantara; the particulars of which, and the following, I will now relate. In the period in which Sávarńi shall be the Manu, the classes of the gods will be Sutapas, Amitábhas, and Mukhyas; twenty-one of each. The seven Rishis will be Díptimat, Gálava, Ráma, Kripa, Drauńi; my son Vyása will be the sixth, and the seventh will be Rishyasringa. The Indra will be Bali, the sinless son of Virochana, who through the favour of Vishńu is actually sovereign of part of Pátála. The royal progeny of Sávarńi will be Virajas, Arvarívas, Nirmoha, and others.