What are the NEC3 prescribed procedures for dealing with subcontractors the Contractor is intending to use?
Just read the clauses within section 26 of the contract and they should be pretty self explanatory.
In simple terms the Contractor has to put forward for acceptance any subcontractor they wish to appoint. The only contractual reason the Project Manager would have to reject them would be that they would not allow the Contractor to provide the works in accordance with the Works Information. This could be they are financially unstable or there are quality/safety concerns about them.
If an NEC form of subcontract is not proposed, then the terms and conditions also have to be issued for acceptance. They should not be appointed until the Project Manager has accepted them.