Follow the rules on Operator's Licence authorisation
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Any vehicle used under an Operator's Licence must be specified on that licence. A vehicle is specified by lodging a Form GV79 A with the appropriate fee at the Traffic Area Office which will issue a disc in the normal way.
The exception is that a vehicle need not be specified on a licence until it has been in the lawful possession of the operator for a period of one calendar month, Vehicles temporarily hired on a day-by-day basis therefore need not be specified and will not have a disc.
However, that does not mean an operator can operate more than the total number of vehicles authorised by spot hiring vehicles for under one month. The total number of vehicles operated on any day must never exceed the total authorised.
from your Operator's Licence and specified on the hirer's licence.
Because the vehicle will have no disc in the window it might attract the attention of the enforcement authorities so you should always keep precise records of the exact period of hire.
Consider giving the driver records of the period of hire to produce if necessary. Some operators even put a disc in the window containing details of the owners of the vehicle, the Operator's Licence number and the period of hire. Finally, remember that even though the vehicle is hired for a short period of time it is still used under your Operator's Licence. The operator still has exactly the same obligation with regard to the condition of the vehicle.