The question is a rather loaded one because fear is generated by different things. Some things a believer can be justifiably afraid of, others arguably not so.
God is to be feared.
Ecclesiastes 12:13 Let us hear the conclusion of the whole matter: Fear God, and keep his commandments: for this is the whole duty of man.
Our fear of God must be greater than our fear of our fellow man, so that we obey God rather than man.
Luke 12:4 And I say unto you my friends, Be not afraid of them that kill the body, and after that have no more that they can do. 5 But I will forewarnyou whom ye shall fear: Fear him, which after he hath killed hath power to cast into hell; yea, I say unto you, Fear him.
Acts 5:29 Then Peter and the other apostles answered and said, We ought to obey God rather than men.
Hebrews 13:6 So that we may boldly say, The Lord is my helper, and I will not fear what man shall do unto me.
Those who have believed the gospel and been baptised into Christ are not promised immunity from troubles in this life.
Ecclesiastes 8:14 There is a vanity which is done upon the earth; that there be just men, unto whom it happeneth according to the work of the wicked; again, there be wicked men, to whom it happeneth according to the work of the righteous: I said that this also is vanity.
Ecclesiastes 9:2 All things come alike to all: there is one event to the righteous, and to the wicked; to the good and to the clean, and to the unclean; to him that sacrificeth, and to him that sacrificeth not: as is the good, so is the sinner; and he that sweareth, as he that feareth an oath.
A life in Christ can bring its own troubles.
Matthew 10:34 Think not that I am come to send peace on earth: I came not to send peace, but a sword. 35 For I am come to set a man at variance against his father, and the daughter against her mother, and the daughter in law against her mother in law. 36 And a man’s foes shall be they of his own household. 37 He that loveth father or mother more than me is not worthy of me: and he that loveth son or daughter more than me is not worthy of me. 38 And he that taketh not his cross, and followeth after me, is not worthy of me.
John 16:2... yea, the time cometh, that whosoever killeth you will think that he doeth God service.
We are to work out our salvation in fear and trembling.
Romans 11:20 Well; because of unbelief they were broken off, and thou standest by faith. Be not highminded, but fear:
Philippians 2:12 Wherefore, my beloved, as ye have always obeyed, not as in my presence only, but now much more in my absence, work out your own salvation with fear and trembling.
Hebrews 4:1 Let us therefore fear, lest, a promise being left us of entering into his rest, any of you should seem to come short of it.
Hebrews 12:28 Wherefore we receiving a kingdom which cannot be moved, let us have grace, whereby we may serve God acceptably with reverence and godly fear: 29 For our God is a consuming fire.
1 Peter 1:17 And if ye call on the Father, who without respect of persons judgeth according to every man’s work, pass the time of your sojourning here in fear:
Christ experienced fear.
Luke 12:50 But I have a baptism to be baptized with; and how am I straitened till it be accomplished!
Matthew 26:39 And he went a little further, and fell on his face, and prayed, saying, O my Father, if it be possible, let this cup pass from me: nevertheless not as I will, but as thou wilt.
Luke 22:44 And being in an agony he prayed more earnestly: and his sweat was as it were great drops of blood falling down to the ground.
Hebrews 5:7 Who in the days of his flesh, when he had offered up prayers and supplications with strong crying and tears unto him that was able to save him from death, and was heard in that he feared;
Paul experienced fear.
1 Corinthians 9:27 But I keep under my body, and bring it into subjection: lest that by any means, when I have preached to others, I myself should be a castaway.
1 Corinthians 2:3 And I was with you in weakness, and in fear, and in much trembling.
2 Corinthians 1:8 For we would not, brethren, have you ignorant of our trouble which came to us in Asia, that we were pressed out of measure, above strength, insomuch that we despaired even of life:
2 Corinthians 7:5 For, when we were come into Macedonia, our flesh had no rest, but we were troubled on every side; without were fightings, within were fears.
The believer looks forward to the day when he/she can serve God without fear.
Luke 1:74 That he would grant unto us, that we being delivered out of the hand of our enemies might serve him without fear,
Belief should alleviate some fear.
Matthew 6:30 Wherefore, if God so clothe the grass of the field, which to day is, and to morrow is cast into the oven, shall he not much more clothe you, O ye of little faith? 31 Therefore take no thought (or be not anxious), saying, What shall we eat? or, What shall we drink? or, Wherewithal shall we be clothed? 32 (For after all these things do the Gentiles seek:) for your heavenly Father knoweth that ye have need of all these things. 33 But seek ye first the kingdom of God, and his righteousness; and all these things shall be added unto you.
Mark 4:40 And he said unto them, Why are ye so fearful? how is it that ye have no faith? 41 And they feared exceedingly, and said one to another, What manner of man is this, that even the wind and the sea obey him?
Luke 12:32 Fear not, little flock; for it is your Father’s good pleasure to give you the kingdom.
Romans 8:15 For ye have not received the spirit of bondage again to fear; but ye have received the Spirit of adoption, whereby we cry, Abba, Father.
We should no longer be afraid of death itself, for we know that we shall be raised again from the dead, but we are probably justified in a fear of our manner of death.
Hebrews 2:15 And deliver them who through fear of death were all their lifetime subject to bondage.
1 Thessalonians 4:13 But I would not have you to be ignorant, brethren, concerning them which are asleep, that ye sorrow not, even as others which have no hope.
Whatever happens to them a believer has the comfort that in Christ all things work towards their salvation.
Romans 8:28 And we know that all things work together for good to them that love God, to them who are the called according to his purpose... 35 Who shall separate us from the love of Christ? shall tribulation, or distress, or persecution, or famine, or nakedness, or peril, or sword? 36 As it is written, For thy sake we are killed all the day long; we are accounted as sheep for the slaughter. 37 Nay, in all these things we are more than conquerors through him that loved us. 38 For I am persuaded, that neither death, nor life, nor angels, nor principalities, nor powers, nor things present, nor things to come, 39 Nor height, nor depth, nor any other creature, shall be able to separate us from the love of God, which is in Christ Jesus our Lord.
We have the promise that we will not be tried above that we are able to bear.
1 Corinthians 10:13 There hath no temptation taken you but such as is common to man: but God is faithful, who will not suffer you to be tempted above that ye are able; but will with the temptation also make a way to escape, that ye may be able to bear it.
The example of Shadrach, Meshach, and Abednego springs to mind. They knew that God was able to save them from the fire, but they had no way of knowing whether he would. In those circumstances their fear would be genuine but they put their service to God above their fear.
Daniel 3:17 If it be so, our God whom we serve is able to deliver us from the burning fiery furnace, and he will deliver us out of thine hand, O king. 18 But if not, be it known unto thee, O king, that we will not serve thy gods, nor worship the golden image which thou hast set up.
We have the example of James who died by the sword of Herod and Peter who was delivered (Acts 12:2-19). From this we see that believers have no guarantee of deliverance from things that are naturally feared.
In conclusion: believers are justified in being afraid of some things and not others, but we must not let our fears take precedence over obedience to the commandments of God.
I hope you have found this helpful.
May God bless you,