"But a certain fearful looking for of judgment and fiery indignation, which shall devour the adversaries." (Hebrews 10: 27)
The context of this verse applies to those who continue to offer animal sacrifices instead of resting in the finality of the Cross.
If we do not believe that Jesus has completed the work of dying for our sins, we will have nothing but a sense of fear and foreboding of evil in our lives.
The Bible tells us that the key to overcoming fear in our lives has nothing to do with what we do, but what He has done for us:
"14In righteousness shalt thou be established: thou shalt be far from oppression; for thou shalt not fear: and from terror; for it shall not come near thee." (Isaiah 54: 14)
Notice that righteousness drives away the oppression, the fear, and the terror:
"17No weapon that is formed against thee shall prosper; and every tongue that shall rise against thee in judgment thou shalt condemn. This is the heritage of the servants of the LORD, and their righteousness is of me, saith the LORD." (Isaiah 54: 17)
This righteousness is accorded to us as a gift, and a gift which He keeps on giving:
"For if by one man's offence death reigned by one; much more they which receive abundance of grace and of the gift of righteousness shall reign in life by one, Jesus Christ." (Romans 5: 17)
When Jesus died on the Cross, He completed a perfect work, granting us His standing:
"For he hath made him to be sin for us, who knew no sin; that we might be made the righteousness of God in him." (2 Corinthians 5: 21)
If we do not believe that Jesus completed a perfect work for us at the Cross, then we will go back to relying on our efforts to achieve righteousness.
Yet this righteousness cannot be achieved, but received.
When we are established in this truth, all fears are put away from us. When we understand the perfect love of God, which has made us one with His Son (As He is, so are we in this world (1 John 4: 17)), then this perfect love casts out all fear.
Believe on Jesus, believe that He did a perfect Work, believe that He is your righteousness, and behold Him removing all fears from your life.