There are a few examples of this kind of yearning in the Old Testament:
Exodus 33:17-18 KJV
17 And the Lord said unto Moses, I will do this thing also that thou hast spoken: for thou hast found grace in my sight, and I know thee by name. 18 And he said, I beseech thee, shew me thy glory.
Psalm 63:1-3 KJV
O God, thou art my God; early will I seek thee: my soul thirsteth for thee, my flesh longeth for thee in a dry and thirsty land, where no water is; 2 To see thy power and thy glory, so as I have seen thee in the sanctuary. 3 Because thy lovingkindness is better than life, my lips shall praise thee.
Psalm 27:4 KJV
One thing have I desired of the Lord, that will I seek after; that I may dwell in the house of the Lord all the days of my life, to behold the beauty of the Lord, and to enquire in his temple
1 Kings 18:36-38 KJV
36 And it came to pass at the time of the offering of the evening sacrifice, that Elijah the prophet came near, and said, Lord God of Abraham, Isaac, and of Israel, let it be known this day that thou art God in Israel, and that I am thy servant, and that I have done all these things at thy word. 37 Hear me, O Lord, hear me, that this people may know that thou art the Lord God, and that thou hast turned their heart back again. 38 Then the fire of the Lord fell, and consumed the burnt sacrifice, and the wood, and the stones, and the dust, and licked up the water that was in the trench.
In the New Testament, the closest to this kind of yearning can be found in Acts 4, although the emphasis here has more to do with the spreading of the gospel:
Acts 4:24-31 KJV
24 And when they heard that, they lifted up their voice to God with one accord, and said, Lord, thou art God, which hast made heaven, and earth, and the sea, and all that in them is: 25 Who by the mouth of thy servant David hast said, Why did the heathen rage, and the people imagine vain things? 26 The kings of the earth stood up, and the rulers were gathered together against the Lord, and against his Christ. 27 For of a truth against thy holy child Jesus, whom thou hast anointed, both Herod, and Pontius Pilate, with the Gentiles, and the people of Israel, were gathered together, 28 For to do whatsoever thy hand and thy counsel determined before to be done. 29 And now, Lord, behold their threatenings: and grant unto thy servants, that with all boldness they may speak thy word, 30 By stretching forth thine hand to heal; and that signs and wonders may be done by the name of thy holy child Jesus. 31 And when they had prayed, the place was shaken where they were assembled together; and they were all filled with the Holy Ghost, and they spake the word of God with boldness.
A similar sentiment is expressed by Paul:
1 Corinthians 2:1-5 KJV
And I, brethren, when I came to you, came not with excellency of speech or of wisdom, declaring unto you the testimony of God. 2 For I determined not to know any thing among you, save Jesus Christ, and him crucified. 3 And I was with you in weakness, and in fear, and in much trembling. 4 And my speech and my preaching was not with enticing words of man's wisdom, but in demonstration of the Spirit and of power: 5 That your faith should not stand in the wisdom of men, but in the power of God.
In Christian mystical traditions, is it common to seek and long for the manifestation of God's power and glory?
Definition of Christian Mystical Traditions
A good source on this topic is List of Christian mystics - Wikipedia. I will quote the introduction of the article, and refer the reader to the article itself for a very comprehensive list of Christian mystics throughout history.
Christian mysticism refers to the development of mystical practices and theory within Christianity. It has often been connected to mystical theology, especially in the Roman Catholic and Orthodox Christianity (both the Eastern Orthodox and Oriental Orthodox traditions).
The attributes and means by which Christian mysticism is studied and practiced are varied. They range from ecstatic visions of the soul's mystical union with God to simple prayerful contemplation of Holy Scripture (i.e., Lectio Divina).
The experiences of mystics are often framed within theological approaches to God, such as Quietism, Pietism, etc.; therefore, in order to aid in the understanding of Christian mysticism, this list includes some philosophers, theologians, anonymous theological books, religious groups and movements whose ideas and practices have had an influence on Christian mystics and the Christian mystical experience.
The Wikipedia article on Christian mysticism also identifies important concepts and categories associated with Christian mysticism, such as Alexandrian mysticism, Monasticism, Desert Fathers, Neo-Platonism, Mystical theology, Cataphatic and apophatic mysticism, Meditation and contemplation, Threefold path, Katharsis, Theoria, Theosis, Alternate models (Augustine, Meister Eckhart, Teresa of Avila, Evelyn Underhill), Latin Catholic mysticism, etc.
In the case of Protestantism, the article Mysticism and the reformation: a brief survey presents an interesting overview on the topic:
A number of influential theologians over the past two centuries have denied that Protestant Christianity has a place for mysticism understood as the mingling of the divine and human natures. Today a more adequate understanding of the mystical element of Christianity as a deeper awareness of God’s presence in the life of believers suggests a new evaluation of the relation of Protestantism and mysticism, beginning Martin Luther, and continuing with figures like Johann Arndt, and a number of the “Spiritual Reformers,” such as Andreas Karlstadt, Sebastian Franck, Valentin Weigel, as well as the theosophical Lutheran Jacob Boehme. This essay is designed to reopen the question of the relation between Protestantism and mysticism.
Another viewpoint is presented by the article Caring for Contemporary Mystics: Pentecostalism and the Mystical Worldview:
Pentecostals can be understood as contemporary Christian mystics, and doing so can aid one in both understanding and caring for them. The task of understanding them is facilitated by this category in that it allows one to inhabit a different mindset from what is typical in contemporary settings. Pentecostalism and charismatic movements work out of distinct, fundamental claims that together work as a kind of worldview, one that operates from a hyperawareness of God’s presence and a sensed empowerment of the mystic’s self. The task of caring for them should honor these claims all the while being open to the Spirit’s presence and work.