We all know there is a gap between Ramayana and Mahabharata, but if so why did Lord Rama's dynasty not participate in Mahabharata? Where were they?
If Mahabharata happened after Ramayana where were the descendants of Rama during Mahabharata?
The descendant of Rama at the time of the Mahabharata was Brihadbala, as described in this chapter of the Srimad Bhagavatam:
The son of Rāmacandra was Kuśa, the son of Kuśa was Atithi, the son of Atithi was Niṣadha, and the son of Niṣadha was Nabha. The son of Nabha was Puṇḍarīka, and from Puṇḍarīka came a son named Kṣemadhanvā. The son of Kṣemadhanvā was Devānīka, Devānīka’s son was Anīha, Anīha’s son was Pāriyātra, and Pāriyātra’s son was Balasthala. The son of Balasthala was Vajranābha, who was said to have been born from the effulgence of the sun-god. The son of Vajranābha was Sagaṇa, and his son was Vidhṛti. The son of Vidhṛti was Hiraṇyanābha, who became a disciple of Jaimini and became a great ācārya of mystic yoga. It is from Hiraṇyanābha that the great saint Yājñavalkya learned the highly elevated system of mystic yoga known as ādhyātma-yoga, which can loosen the knots of material attachment in the heart. The son of Hiraṇyanābha was Puṣpa, and the son of Puṣpa was Dhruvasandhi. The son of Dhruvasandhi was Sudarśana, whose son was Agnivarṇa. The son of Agnivarṇa was named Śīghra, and his son was Maru. Having achieved perfection in the power of mystic yoga, Maru still lives in a place known as Kalāpa-grāma. At the end of Kali-yuga, he will revive the lost Sūrya dynasty by begetting a son. From Maru was born a son named Prasuśruta, from Prasuśruta came Sandhi, from Sandhi came Amarṣaṇa, and from Amarṣaṇa a son named Mahasvān. From Mahasvān, Viśvabāhu took his birth. From Viśvabāhu came a son named Prasenajit, from Prasenajit came Takṣaka, and from Takṣaka came Bṛhadbala, who was killed in a fight by your father.
When Shuka says "your father", he's addressing Parikshit, so he's referring to Abhimanyu. And indeed, Abhimanyu killed Brihadbala in the Chakravyuha right before he, as described in this chapter of the Drona Parvati of the Mahabharata:
Then Drona, Kripa and Karna and Drona's son, and the king of the Kosalas, and Kritavarman, these six car-warriors surrounded the son of Subhadra. Having surrounded that child all those great car-warriors--too many for him although he was contending to the utmost of his power, deprived him of his car. After he had been deprived of his car, Dussasana's son, though he himself had a hair-breadth escape, succeeded, as chance would have it, in making Abhimanyu, meet with his end. As regards Abhimanyu, he, having slain many thousands of men and steeds and elephants, and eight thousand cars, and once more nine hundred elephants, two thousand princes, and a large number of heroic warriors unknown to fame, and dispatching in that battle king Vrihadvala also to heaven, at last, through ill luck, met with his own death.
During the great war, the [then] descendent of RAma, sided with Kaurava-s.
Kosala Kingdom is believed to be Lord RAma's kingdom.
Kosala Proper or Uttara Kosala is the kingdom of the celebrated personality of Treta Yuga, Raghava Rama. ... Rama's brother Bharata, colonized the Gandhara kingdom and founded the city of Takshasila there. Gandhara lies close to Kekeya Kingdom, the native kingdom of Bharata's mother, Kaikeyi. Rama's second brother Lakshmana founded the city of Lakshmanapura near river Ganges which is now known as Lucknow. He colonized the Vanga kingdom and founded the city of Chandrakanta there. Rama's youngest brother Satrughna destroyed the forest called Madhu and founded the city of Mathura which later became the capital of the Surasena Kingdom.
Particular to your question, the king of Kosala should be considered as the descendent of Raghu Vamsha (i.e. RAma). During the great war, Brihadbala was 1 of king & he sided with Kaurava. He was killed by Abhimanyu:
Nishadha king Nala's friend Rituparna was a ruler of Kosala. Brihadbala another ruler of Kosala during Dwapara Yuga, took part in Mahabharata war and was killed by Abhimanyu, the son of Arjuna.
Here is the proper reference from Stri VilApa Parva:
There, again, those other ladies, surrounding their lord, the ruler of the Kosalas, prince Brihadbala, are indulging in loud wails. Engaged in plucking from his body the shafts with which it was pierced by Abhimanyu with the full might of his arms, those ladies are repeatedly losing their senses.
Here is another fancy article, but I am not sure if it can be cited here.