"sole supplier" is correct and usable in written English.
This refers to a company that is the only supplier of a product or service. For example, "We are the sole supplier of frozen custard for the city."
It is the sole supplier of the cellphone service.
Adidas has been the sole supplier of balls for the World Cup since 1970.
"It puts us in a very difficult position to be the sole supplier.
It is the sole supplier of chips for Mi crosoft's Xbox games console.
Mirant had been the sole supplier to Pepco in Washington and Maryland.
Both said they would bid to become the sole supplier for Kmart's 2,100 stores.
Executives said that the company would not remain so dependent on a sole supplier.
Fuji Heavy Industries is the sole supplier of the Dreamliner's centre wing box, connecting its wings to the fuselage.
These purchases have established an integrated power service area in which the TVA is the sole supplier of power.
Pirelli have replaced Bridgestone as Formula One's sole supplier and are still formulating the construction and compounds.
"I closed down and let everyone start their own businesses with us as the sole supplier" of plastic, he said.
