You would have signed a letter to appoint the consultant with certain terms and conditions. Is there not a termination clause in it stipulating the notice period?
The common industry practice is for any such appointment, there will be a written term that includes the termination clause so that both parties are clear about it to avoid any such disputes. Generally, a notice period of 15 to 30 days is mentioned in such engagements.
If the termination of services is for the convenience of the parties, usually it will be with 30 days’ written notice.
If the termination is for any cause (e.g., non-performance, misconduct, etc.) then the employer stipulates either the termination with immediate effect or minimal no. of days notice and ends the service.