Non-compete Clause and Legal Considerations
A non-compete clause militates against the fundamental right guaranteed by the Constitution, granting freedom to pursue business, profession, or avocation of one's choice, subject to reasonable restrictions in this regard. As per the Contract Act of 1872, there cannot be a valid contract that goes against the statutes. Thus, while there cannot be a total embargo on such employment, a limited restriction for 2-3 years for seeking employment with competing firms in the employment contract has been upheld by the courts. You may consider framing your non-compete clause in the above light.
Implementing a Non-compete Clause
Since there is no such clause, you may have to issue an order amending the service conditions accordingly. This has to be brought to the attention of all employees.
Having a non-compete clause is one thing, but implementing it is the bigger challenge. How are you going to keep track of the exited employees? You may limit the scope of the non-compete clause to the critical resource persons, and if so, inform them in person and take their acknowledgment of the order in this regard.