I wonder why there is no context about Lord Rama previous incarnation of Lord Vishnu before Lord Krishna. Only Hanuman is mentioned in the story.
Rama is mentioned in the Bhagavad Gita which is a part of the Mahabharata.
pavanaḥ pavatām asmi
rāmaḥ śastra-bhṛtām aham
jhaṣāṇāṁ makaraś cāsmi
srotasām asmi jāhnavī
Meaning:- Of puriﬁers I am the wind, of the wielders of weapons I am Rāma, of ﬁshes I am the shark, and of ﬂowing rivers I am the Ganges.
Rama is mentioned many times in the Mahabharata:
As I discuss in this answer, once while the Pandavas and Draupadi while living in the forest, Duhsala's husband Jayadratha kidnapped Draupadi, and the Pandavas rescue her. Afterwards, Yudhishthira was despondent that he allowed his wife to be kidnapped, so he asked Markandeya whether there was anyone in history who was as miserable as he was. Markandeya said there was such an individual, Rama:
O bull of the Bharata race, even Rama suffered unparalleled misery, for the evil-minded Ravana, king of the Rakshasas, having recourse to deceit and overpowering the vulture Jatayu, forcibly carried away his wife Sita from his asylum in the woods. Indeed, Rama, with the help of Sugriva, brought her back, constructing a bridge across the sea, and consuming Lanka with his keen-edged arrows.
In the Drona Parva of the Mahabharata, Yudhisthira is despondent because of the death of Bhima's son Ghatotkacha, so the sage Vyasa comes to the battlefield and tells Yudhisthira about a dialogue that the sage Narada had with a king named Srinjaya after Srinjaya's son had died. Narada tells Srinjaya that he shouldn't feel so bad that his son has died, when death has even befallen illustrious people of extraordinary achievement. In this chapter of the Drona Parva, Narada cites Rama as one such example:
Rama, the son of Dasaratha, O Srinjaya, we hear, fell a prey to death. His subjects were as much delighted with him, as a sire is delighted with the children of his loins. Endued with immeasurable energy, countless virtues were there in him. Of unfading glory, Rama, the elder brother of Lakshmana, at the command of his father, lived for fourteen years in the woods, with his wife. That bull among men slew in Janasthana fourteen thousand Rakshasas for the protection of the ascetics. While dwelling there, the Rakshasa called Ravana, beguiling both him and his companion (Lakshmana) abducted his wife, the princess of Videha. Like the Three-eyed (Mahadeva), in days of old, slaying (the Asura) Andhaka, Rama in wrath slew in battle that offender of Pulastya's race who had never before been vanquished by any foe. Indeed, the mighty-armed Rama slew in battle that descendant of Pulastya's race with all his kinsmen and followers, that Rakshasa who was incapable of being slain by the gods and the Asuras together, that wretch who was a thorn unto the gods and the Brahmanas. In consequence of his affectionate treatment of his subjects, the celestials worshipped Rama. Filling the entire earth with his achievements, he was much applauded even by the celestial Rishis.... Youthful in shape, of a dark-blue hue, of red eyes, possessed of the tread of an infuriated elephant, with arms reaching down to the knees, and beautiful and massive, of leonine shoulders, of great strength, and beloved by all creatures, Rama ruled his kingdom for eleven thousand years. His subjects always uttered his name. While Rama ruled his kingdom, the world became extremely beautiful. Taking at last his four kinds of subjects with him Rama went to heaven, having established his own line consisting of eight houses on the earth. When even he died, O Srinjaya, who was superior to thee in respect of the four cardinal virtues and superior to thy son, thou shouldst not lament, saying 'Oh, Swaitya, Oh, Swaitya,' for thy son who performed no sacrifice and made no sacrificial present.
In this chapter of the Shanti Parva of the Mahabharata, Vishnu's Aniruddha form (which I discuss here) tells Narada about the different incarnations he is going to take in future, and in particular he says this:
Towards the close of Treta and the beginning of Dwapara, I shall take birth as Rama, the son of Dasaratha in Iskshaku's royal line. At that time, the two Rishis viz., the two sons of Prajapati, called by the names of Ekata and Dwita, will in consequence of the injury done by them unto their brother Trita, have to take birth as apes, losing the beauty of the human form. Those apes that shall take birth in the race of Ekata and Dwita, shall become endued with great strength and mighty energy and will equal Sakra himself in prowess. All those apes, O regenerate one, will become my allies for accomplishing the business of the deities. I shall then slay the terrible lord of the Rakshasas, that wretch of Pulastya's race, viz., the fierce Ravana, that throne of all the worlds, together with all his children and followers.
These are just three prominent examples, but there are many others.