The word apathy, per se, is not used in the Bible. It uses many other varieties though.
Hardened heart is used so many times in the Old Testament in reference to Pharaoh and the Israelites as they wandered in the desert. Both Pharaoh and the Israelites saw first hand God's might acts and still chose not to believe or just grumble and complain against him. This is a form of apathy. They had knowledge of God and his power but didn't care.
Lukewarm is another term used by Jesus in the letter to the church of Laodicea.
I know your deeds, that you are neither cold nor hot. I wish you were one or the other! So, because you are lukewarm--neither hot or cold--I am about to spit you out of my mouth! Revelation 3:15-16
Being lukewarm is a lack of forward movement, complacency, lackadaisical. There is no action being taken for one reason or another, but it is seen as apathetic. When you are apathetic as a Christian, you aren't growing and bearing fruit. In John 15, Jesus pleads for us to remain in him, so that he will be in use growing so that we bear fruit. He will even prune us so we bear more fruit and become better and better. We do not want to be the apathetic vine that withers and is cut off to be thrown in the fire to burn.
Am I always bearing fruit? Definitely, not. I do go through seasons and I feel it in my heart when Jesus begins tugging on that branch saying it might be time to prune you, Jennifer!
We must heed the warning, wake up and take action!
This is all the more urgent, for you know how late it is; time is running out. Wake up for our salvation is nearer now than when we first believed. Romans 13:11
Arise! Shine, for your light has come and the glory of The Lord has risen upon you. Isaiah 60:1
As I see it, the opposite of apathy in Christ is enthusiasm. The Bible has much to say on this subject!
Never be lazy, but work hard and serve The Lord enthusiastically. Romans 12:11
Whatever your hand finds to do, do it with all your might. Ecclesiastes 9:10.
Work with enthusiasm, as though you were working for The Lord rather than for people. Ephesians 6:7
If you do not serve The Lord your God with joy and enthusiasm for the abundant benefits you have received, you will serve your enemies. Deuteronomy 28:47
What is the fix for apathy in The Lord? Be in his word. Pray. Focus on Christ and have a servant's heart. If we are filled with his love and joy, there is no room for apathy.
Rejoice in The Lord always and again I say rejoice! Philippians 4:4
Rejoice always. Pray continually, give thanks in all circumstances; for this is God's will for you in Jesus Christ. 1 Thessalonians 5:16-18