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Yes, this is a principle of great importance to The Church of Jesus Christ of Latter-day Saints.
Recent Teachings
In an April 2020 global conference, church president Russell M Nelson gave a discourse entitled Hear Him, including the following remarks:
We also hear Him more clearly as we refine our ability to recognize the whisperings of the Holy Ghost. It has never been more imperative to know how the Spirit speaks to you than right now. In the Godhead, the Holy Ghost is the messenger. He will bring thoughts to your mind which the Father and Son want you to receive. He is the Comforter. He will bring a feeling of peace to your heart. He testifies of truth and will confirm what is true as you hear and read the word of the Lord.
I renew my plea for you to do whatever it takes to increase your spiritual capacity to receive personal revelation. (see here)
Two years prior he also gave an address discussing how & why to come to recognize revelation from God. See Revelation for the Church, Revelation for Our Lives
The April 2020 sermon led to a hashtag among Latter-day Saints #HearHim (referring to hearing God) that has prompted many responses in which people have described what they do to hear Him. My own #HearHim comments are here.
Passages from canonized scripture
One of the Book of Mormon passages most commonly cited by missionaries of The Church of Jesus Christ of Latter-day Saints is Moroni 10:4-5, which specifically calls upon people to seek confirmation from God regarding the book:
4 And when ye shall receive these things, I would exhort you that ye would ask God, the Eternal Father, in the name of Christ, if these things are not true; and if ye shall ask with a sincere heart, with real intent, having faith in Christ, he will manifest the truth of it unto you, by the power of the Holy Ghost.'
5 And by the power of the Holy Ghost ye may know the truth of all things.
One of the passages used to describe what revelation from God feels like is Doctrine & Covenants 11:12-13:
12 And now, verily, verily, I say unto thee, put your trust in that Spirit which leadeth to do good—yea, to do justly, to walk humbly, to judge righteously; and this is my Spirit.
13 Verily, verily, I say unto you, I will impart unto you of my Spirit, which shall enlighten your mind, which shall fill your soul with joy;
Conclusion
Members of the Church of Jesus Christ of Latter-day Saints believe that God speaks today as He did in the past, and the church actively teaches its members to seek revelation from God for the areas of responsibility He has given them.
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In the Lutheran tradition, a more nuanced approach is taken on the matter. That is to say there is the possibility of ongoing inspiration, but one must hear it (i.e. discern it) as a lower level of inspiration than the Scripture edited by the Old Testament Prophets & New Testament canonical Apostles.
For example, the 19th century Lutheran theologian Franz Pieper, writes in his Christian Dogmatics:
The question has often been asked whether divine revelations pertaining to external events in Church or world might not be given to individual persons in our time. It does not contradict Scripture to admit the possibility and fact of such revelations. But it is contrary to Scripture to assume that new revelations on doctrine will be given; the revelation of doctrine has come to an end with the Word of the Apostles and Prophets. (Franz Pieper, Christian Dogmatics, Vol.1, p. 211)
After providing Biblical examples like Acts 11:27-28; 21:10-11, Franz Pieper also appeals to the Wittenburg theologian, Friedrich Balduin (1575-1627 A.D.):
We do not doubt that God to this day at times reveals to men future things pertaining to the state of the Church or the State, to be announced for the use of men. (Christian Dogmatics, Vol, 1, p. 211)
Having said the above, Franz Pieper qualifies this by quoting the 17th century Wittenburg theologian, John Quenstedt:
We must distinguish between revelations which pertain to, or attack, an article of faith, and those which concern the state of the Church or the State, social life, and future events; the first we repudiate; the latter, however, some hold, are not to be urged with any necessity of believing, nevertheless are not to be rashly rejected. (Franz Pieper, Christian Dogmatics, Vol. 1, p. 211)
The Lutheran position appeals to both Scripture and the early church's view of the continuation of low level inspirational prophetic gifts. For example, St. Jerome reacted to the Montanist movement in the early church by writing:
...if the Montanists reply that Philip’s four daughters prophesied (Acts xxi. 9) at a later date, and that a prophet is mentioned named Agabus, (Acts xi. 28; xxi. 10, 11 and that in the partition of the spirit, prophets are spoken of as well as apostles, teachers and others, we do not so much reject prophecy—for this is attested by the passion of the Lord—as refuse to receive prophets whose utterances fail to accord with the Scriptures old and new. - St. Jerome (385 A.D., Letter XLI: To Marcella)