The strait gate one must enter is repentance and baptism into Christ's divinely authorized Church. Christ set up His one true Church in the New Testament and set Peter as the chief Apostle who is the prophet of the Church, and James and John filled out the First Presidency, and then the Quorum of 12 Apostles. These 15 Apostles, all of whom are prophets, form the top leadership of the Church. All held the Melchizadek priesthood, all held the keys of the kingdom of God on the earth, and were directed by revelation from the living resurrected Christ. The strait gate in New Testament times was repentance and baptism into this the one true Church which is the eccliastical kingdom of God on the earth. If there were hundreds of other different Christian sects led by false Christian leaders all claiming the true Church of the apostles is an imposter and many people embraced these other Christian churches then they would not have entered into the strait gate.
The great news is that Christ's divinely authorized Church was restored by God in these last days. The Church of Jesus Christ of Latter Day Saints is guided by a chief Apostle who is the Prophet, his two counselors that form the First Presidency of the Church, and a Quorum of 12 Apostles. They hold the Melcizadek priesthood, they hold keys of the Kingdom of God on the earth which will never again be taken off the earth, and are guided by the living resurrected Christ by direct revelation. They are special witnesses of Christ on earth as they testify He lives because they have been visited by Him.
https://www.lds.org/church/leaders/first-presidency?lang=eng
https://www.lds.org/church/leaders/quorum-of-the-twelve-apostles?lang=eng
17 Wherefore, do the things which I have told you I have seen that your Lord and your Redeemer should do; for, for this cause have they been shown unto me, that ye might know the gate by which ye should enter. For the gate by which ye should enter is repentance and baptism by water; and then cometh a remission of your sins by fire and by the Holy Ghost.
18 And then are ye in this strait and narrow path which leads to eternal life; yea, ye have entered in by the gate; ye have done according to the commandments of the Father and the Son; and ye have received the Holy Ghost, which witnesses of the Father and the Son, unto the fulfilling of the promise which he hath made, that if ye entered in by the way ye should receive.
19 And now, my beloved brethren, after ye have gotten into this strait and narrow path, I would ask if all is done? Behold, I say unto you, Nay; for ye have not come thus far save it were by the word of Christ with unshaken faith in him, relying wholly upon the merits of him who is mighty to save.
20 Wherefore, ye must press forward with a steadfastness in Christ, having a perfect brightness of hope, and a love of God and of all men. Wherefore, if ye shall press forward, feasting upon the word of Christ, and endure to the end, behold, thus saith the Father: Ye shall have eternal life.
21 And now, behold, my beloved brethren, this is the way; and there is none other way nor name given under heaven whereby man can be saved in the kingdom of God. And now, behold, this is the doctrine of Christ, and the only and true doctrine of the Father, and of the Son, and of the Holy Ghost, which is one God, without end. Amen. (2 Nephi 31:17-21)