Eukaireo means to have a good opportunity, to find the right moment, to have leisure for something. It combines eu (well) and kairos (the right time/season) with a verbal suffix, creating the idea of having a kairos moment available. The word speaks of windows of opportunity — time that is ripe for a particular action.
The theology of time in Scripture distinguishes chronos (clock time) from kairos (right-time, opportunity). Eukaireo names the experience of having a kairos available. Mark 6:31 uses it when Jesus calls his disciples to come away and rest — they finally had time to eat. Acts 17:21 uses it ironically for the Athenians who spent all their time in philosophical discussion. Ephesians 5:16 commands believers to 'make the most of every opportunity [kairos]' — to seize eukaireo moments for the gospel and for righteousness.