Our Gemara on Amud Aleph discusses the permissibility to listen to a bas kol, a heavenly voice, and that it is not considered divination:

And Rabbi Shefatya said that Rabbi Yoḥanan said: If one was deliberating about whether to do a certain action, and a Divine Voice indicated what he should do, from where is it derived that one may make use of a Divine Voice and rely upon it? As it is stated: “And your ears shall hear a word behind you saying: This is the way, walk in it” (Isaiah 30:21).

The gemara Sanhedrin (11a) discusses bas kol a bit more:

The Sages taught: After the last of the prophets, Haggai, Zechariah, and Malachi, died, the Divine Spirit of prophetic revelation departed from the Jewish people. But nevertheless, they were still utilizing a Divine Voice, which they heard as a “daughter of a voice” from God. 

What actually is a Bas Kol?  Most people, who have watched way too many movies, imagine it to be a thundering voice of God, kind of like Earl Jone’s voice as Darth Vader.  However, this is absolutely incorrect.  Actually, like many theological truths, a bas kol is heard in a subtle manner.   

Tosafos Yom Tov (Mishna Yevamos 16:6) reviews some of the opinions about a bas kol.  It is a minor form of prophecy, still present after we no longer have prophecy. He quotes Tosafos (Sanhedrin 11a) that it is an echo of an original voice, hence it is called a daughter of a voice. Furthermore, Tosafos Yom Tov observes that it is known as a daughter of a voice, not a son of a voice, to connote its relative weakness, in comparison to prophecy. 

My friends, often we can still hear God’s will if we want to, however do not expect it to come in a loud thundering voice from heaven. Instead it will come to you as a quiet, low voice, as described in Melachim I (19:12).  When the Rambam describes the various levels of prophecy in his Guide for the Perplexed (II:45), he starts from the lowest to the highest.  Listen carefully to his description of the first two levels:

The first degree of prophecy consists in the divine assistance which is given to a person, and induces and encourages him to do something good and grand, e.g., to deliver a congregation of good men from the hands of evildoers; to save one noble person, or to bring happiness to a large number of people; he finds in himself the cause that moves and urges him to this deed. This degree of divine influence is called "the spirit of the Lord"; and of the person who is under that influence we say that the spirit of the Lord came upon him, clothed him, or rested upon him, or the Lord was with him, and the like.This faculty did not cause any of the above-named persons to speak on a certain subject, for it only aims at encouraging the person who possesses it to action; it does not encourage him to do everything, but only to help either a distinguished man or a whole congregation when oppressed, or to do something that leads to that end. just as not an who have a true dream are prophets, so it cannot be said of every one who is assisted in a certain undertaking, as in the acquisition of property, or of some other personal advantage, that the spirit of the Lord came upon him, or that the Lord was with him, or that he performed his actions by the holy spirit. We only apply such phrases to those who have accomplished something very good and grand, or something that leads to that end; e.g., the success of Joseph in the house of the Egyptian, which was the first cause leading evidently to great events that occurred subsequently.

The second degree is this: A person feels as if something came upon him, and as if he had received a new power that encourages him to speak. He treats of science, or composes hymns, exhorts his fellow-men, discusses political and theological problems; all this he does while awake, and in the full possession of his senses. Such a person is said to speak by the holy spirit…I have, therefore, pointed out to you, that the prophecy revealed to Daniel and Solomon, although they saw an angel in the dream, was not considered by them as a perfect prophecy, but as a dream containing correct information. They belonged to the class of men that spoke, inspired by the ruaḥ ha-kodesh, "the holy spirit." Also in the order of the holy writings, no distinction is made between the books of Proverbs, Ecclesiastes, Daniel, Psalms, Ruth, and Esther; they are all written by divine inspiration. The authors of all these books are called prophets in the more general sense of the term.

It is important to note that Rambam does not consider these first two levels as prophecy.  Thus, the distinction of the Gemara in Sanhedrin that we no longer have prophecy absolutely does not apply to these intuitions nor to a sense that one is called upon to do greatness. I say this to all of you in that we should realize that even today, a person can correctly perceive that God is calling upon them and motivating them toward a lofty or important task.  Running away from a sense that this is possible is like Yonah running away to Nineveh.