Dhruva Maharaja fought with Yakshas. When and at what instance did this happen?
Dhruva Maharaja fight with Yakshas is described in SB 4.10. He fought because his brother Uttama was killed by a Yaksha.
uttamas tv akṛtodvāho
tan-mātāsya gatiṁ gatā (3)
Dhruva Mahārāja’s younger brother Uttama, who was still unmarried, once went on a hunting excursion and was killed by a powerful Yakṣa in the Himālaya Mountains. Along with him, his mother, Suruci, also followed the path of her son [she died].
dhruvo bhrātṛ-vadhaṁ śrutvā
jaitraṁ syandanam āsthāya
gataḥ puṇya-janālayam (4)
When Dhruva Mahārāja heard of the killing of his brother Uttama by the Yakṣas in the Himālaya Mountains, being overwhelmed with lamentation and anger, he got on his chariot and went out for victory over the city of the Yakṣas, Alakāpurī.
Continuation to Triyugi Narayan Mani's answer:
When Dhruva Mahārāja heard of the killing of his brother Uttama by the Yakṣas in the Himālaya Mountains, being overwhelmed with lamentation and anger, he got on his chariot and went out for victory over the city of the Yakṣas, Alakāpurī. Dhruva Mahārāja went to the northern direction of the Himālayan range. In a valley he saw a city full of ghostly persons who were followers of Lord Śiva. As soon as Dhruva Mahārāja reached Alakāpurī, he immediately blew his conchshell, and the sound reverberated throughout the entire sky and in every direction. The wives of the Yakṣas became very much frightened. From their eyes it was apparent that they were full of anxiety.
The greatly powerful heroes of the Yakṣas, unable to tolerate the resounding vibration of the conchshell of Dhruva Mahārāja, came forth from their city with weapons and attacked Dhruva.
Dhruva Mahārāja, who was a great charioteer and certainly a great bowman also, immediately began to kill them by simultaneously discharging arrows three at a time.
When the heroes of the Yakṣas saw that all their heads were being thus threatened by Dhruva Mahārāja, they could very easily understand their awkward position, and they concluded that they would certainly be defeated. But, as heroes, they lauded the action of Dhruva. The Yakṣa soldiers were 130,000 strong, all greatly angry and all desiring to defeat the wonderful activities of Dhruva Mahārāja. With full strength they showered upon Mahārāja Dhruva, along with his chariot and charioteer, various types of feathered arrows, parighas [iron bludgeons], nistriṁśas [swords], prāsaśūlas [tridents], paraśvadhas [lances], śaktis [pikes], ṛṣṭis [spears] and bhuśuṇḍī weapons.
Dhruva Mahārāja was completely covered by an incessant shower of weapons, just as a mountain is covered by incessant rainfall. All the Siddhas from the higher planetary systems were observing the fight from the sky, and when they saw that Dhruva Mahārāja had been covered by the incessant arrows of the enemy, they roared tumultuously, “The grandson of Manu, Dhruva, is now lost!” They cried that Dhruva Mahārāja was just like the sun and that now he had set within the ocean of the Yakṣas.
The Yakṣas, being temporarily victorious, exclaimed that they had conquered Dhruva Mahārāja. But in the meantime Dhruva’s chariot suddenly appeared, just as the sun suddenly appears from within foggy mist. Dhruva Mahārāja’s bow and arrows twanged and hissed, causing lamentation in the hearts of his enemies. He began to shoot incessant arrows, shattering all their different weapons, just as the blasting wind scatters the assembled clouds in the sky.
The sharp arrows released from the bow of Dhruva Mahārāja pierced the shields and bodies of the enemy, like the thunderbolts released by the King of heaven, which dismantle the bodies of the mountains.
Source : Srimad Bagavatham 4.10.4 to 4.10.17