If someone asks you about your faith, then you should respond. 1 Peter 3:
See also What is my calling?.
The collective church has the responsibility to spread the gospel to the world. Matthew 28:15 But in your hearts honor Christ the Lord as holy, always being prepared to make a defense to anyone who asks you for a reason for the hope that is in you; yet do it with gentleness and respect,
If you are in a place where no one knows about the gospel, then you should make an effort to spread the gospel, Acts 8:19 Go therefore and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit,
Some believers are gifted to evangelize, Ephesians 4:4 Now those who were scattered went about preaching the word.
Not every believer is required to spread the gospel actively. I tell people about the good news occasionally, but I do not do it actively. According to Paul, evangelists are the ones most actively spreading the gospel.11 And he gave the apostles, the prophets, the evangelists, the shepherds and teachers, 12 to equip the saints for the work of ministry, for building up the body of Christ
See also What is my calling?.