I want to know if there are details of the fight between Chitrangada (brother of Bhishma) and the gandharva with the same name.
The details can be found in Mahabharata: Adi Parva: Sambhava Parva:
And after Santanu had ascended to heaven. Bhishma, placing himself under the command of Satyavati, installed that suppressor of foes, viz., Chitrangada, on the throne, who, having soon vanquished by his prowess all monarchs, considered not any man as his equal.
And beholding that he could vanquish men, Asuras, and the very gods, his namesake, the powerful king of the Gandharvas, approached him for an encounter. Between that Gandharva and that foremost one of the Kurus, who were both very powerful, there occurred on the field of Kurukshetra a fierce combat which lasted full three years on the banks of the Saraswati. In that terrible encounter characterised by thick showers of weapons and in which the combatants ground each other fiercely, the Gandharva, who had greater prowess or strategic deception, slew the Kuru prince. Having slain Chitrangada--that first of men and oppressor of foes--the Gandharva ascended to heaven.
When that tiger among men endued with great prowess was slain, Bhishma, the son of Santanu, performed, O king, all his obsequies.