Quran mentions other nations, Prophets as well as saintly personalities which are not mentioned in the Bible. Please note that the purpose of the Quran is always brief and to the point to get the message across to those who seek guidance and not get them involved in identification details of the personalities, unnecessary details about nations and their stories unless there is some important lesson to learn therefrom. Quran is very concise and to the point. Unlike Bible which consists of 67 something books, Quran is only a single book with 6000 and some verses.
Quranic Prophets not mentioned in the Bible
Ancient Arabian Prophets such as Prophet Hud (a.s) are mentioned in the Quran but not explicitly mentioned in the Bible. There is also mentioned Prophet Salih (a.s) who is not mentioned in the Bible. He was sent to the people of the Mada'in Saleh, a region in the Hejaz area of present day Saudi Arabia (Image below - Al-Hijr or Mada'in Salih in Hejaz, modern day Saudi Arabia):
(Al Quran 7:74) "and settled you firmly on earth, so that you [are able to] build for yourselves castles on its plains and hew out mountains [to serve you] as dwellings: remember, then, God's blessings, and do not act wickedly on earth by spreading corruption."
Reference to Prophet Zoroaster (Zarathushtra), who is absent from the Bible, is referred to in the Quran. According to many Islamic scholars he is referred in the following verse: (Al Quran 2:17) "The likeness of them is as the likeness of one who set to kindle a fire; so, as soon as it illuminated whatever is around him, Allah went away with their light, (i.e., took away their light) and left them in darkness (where) they do not behold (anything)." In the Parsi (Persian Religious) scriptures he is said to have light fire when taking pledge from the Persians as a symbol that would keep them as a reminder of obedience to Allah ﷻ but they were misled and started to worship the fire instead of their Creator.
Quranic nations not mentioned in the Bible
Many nations are mentioned in the Quran to whom Allah ﷻ sent Prophets with revelation and only the name of that nation is mentioned such as: (Al Quran 25:38) "And [remember how We punished the tribes of] 'Ad and Thamud, and the people of Ar-Rass," (Al Quran 44:37) "Are they, then, better than the people of Tubba', and those before them, whom We destroyed because they were truly lost in [the same) sin?" As per famous 20th century Islamic scholar Muhammad Assad, Ar-Rass is a town of that exists to this day in the Central-Arabian province of Al-Qasim; in the ancient times it seems to have been inhabited by descendants of the Nabataean tribe of Thamud, the nation to whom was sent Prophet Salih (alaihi salaam). Their descendants were also sent a Prophet and punished for their wrongdoings but their details are not mentioned as its not necessary as long as the point is made clear. Ar Rass means wells of water and some scholars say this may be reference to Indus Valley civilizations that created wells that Arabs referred to in the ancient times as "people of Ar Rass". Qaumun Tubban (people of Tubba) is a reference to the nation that were ruled by a long succession of Himyari Kings of Yemen whose people were disobedient to Allah ﷻ and were subsequently vanished from the pages of history with time.
Saintly Quranic personalities not mentioned in the Bible
In Surah Kahf the brief account of young men and the cave is mentioned who are not mentioned in the Bible, some references are found to them in Christian tradition as ‘seven sleepers’ but not all Christians accept that as they are not mentioned anywhere in Gospel or New Testament (of Bible). They separated themselves for the sake of Allah ﷻ from their misguided and materialistic environment. References are made to Luqman al Hakim (The Sage), who some scholars equate him to Greek Aesop, who teaches his son the characteristics of a believer something all believers can learn from. Mention has been made about Khidr (alaihi salaam) whose a mystic that carries sacred knowledge which is beyond the apparent that majority carry. His location at the conjunction of the two seas (Al Quran 18:60) may have been somewhere between the conjunction of Atlantic ocean with Mediterranean or Mediterranean with Black Sea. Quran also mentions Dhul Qarnayn (alaihi salaam), a Prophet King who ruled with justice, punishing those who oppress and exploit while protecting those who are good. He built a wall in Central Asia, the historic lands of the Turks, to prevent Gog and Magog tribes from plundering and destroying the weaker tribes. The Bible mentions Gog and Magog but does not mentioned Dhul Qarnayn (alaihi salaam).
References to Prophets & nations in the Hadith/Sunnah literature
The following verses was revealed to Prophet Muhammad ﷺ in the first instance: (Al Quran 40:78) "And, indeed, [O Muhammad,] We sent forth Messengers before your time; some of them We have mentioned to you, and some of them We have not mentioned to you." The meaning of this verse can be found in an authentic hadith when the Prophet was inquired of how many prophets lived in the past to which he replied "Allah sent 124000 Prophets out of which 313 were messengers." This hadith informs us that Prophet was aware of many personalities and their names in addition to those mentioned in the Quran and of many he was unaware unless Allah taught him. The hadith literature includes plenty references of such personalities, some are mentioned by name and others are not. For instance Allah's Messenger (ﷺ) saying: "An ant bit a Prophet amongst the Prophets, and he ordered that the place of the ants be burnt. So, Allah inspired to him, 'It is because one ant bit you that you burnt a nation amongst the nations that glorify Allah?" (Sahih Al Bukhari - Source Sayings and Teachings of Prophet Muhammad (صلى الله عليه و سلم) Who was this Prophet is not of concern but the ethical lesson being taught of how to treat creatures of Allah ﷻ, even as little as ant, is of concern. Where these personalities dwelt or lived, their details, is of no concern to a believer as long as we learn lessons from their accounts.