1to have no opportunity
2no way (of doing sth)
3no chance
4no connection
5not placed (in a competition)
6(in pop lyrics) no chance of love, no place to be together etc
Example
yǒu yuán有缘qiān千lǐ里lái来xiāng相huì会，wú yuán无缘duì miàn对面bù不xiāng相féng逢。
有缘千里来相会，无缘对面不相逢。
Those fated to meet will do so regardless of distance. Those not fated will not, even if they are across from one another.