What a chemical engineer should do if he doesn't get his relevant job in the first 3 years? Because after 3 years he is no more fresh or experienced.

Learn more, get a specialization certification, learn about softwares such as aspen, hysis, flarenet, etc. Expand one's knowledge base to identify what kind of skills employers want. Or, they can study more for higher education and become teacher or trainer. 

Should looking for job that less than Engineering like Lab Chemist ..etc

Goodluck