Electrical Certificate & Contract Holder Change - Do You Need a New One?

Please confirm; if we already have a 5-year electric certificate and a contract holder vacates, do we need to have another carried out for a new occupier? Regardless of the time left on the 5-year certificate.  
The government site explaining ECIRs seems a bit confusing.

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Electrical Safety and Electrical Goods

Landlords should have a clear understanding of their responsibilities regarding electrical installations and appliances