There is complete flexibility over what contract you use to engage your subcontractor. You just need to get acceptance from the TSC service manager of the name of the proposed subcontractor and the proposed subcontract conditions in accordance with clauses 26.2 and 26.3 of the TSC. In respect of accepting the proposed subcontract conditions, this will be subject to the exceptions stated in clause 26.3.
You could choose to use an NEC3 or NEC4 form of contract as the subcontract, depending on the nature of the service to be subcontracted. The NEC3 suite of contracts did not contain a TSS but one was introduced into the NEC4 suite. The NEC3 suite did however contain an Engineering and Construction Subcontract (ECS) and Engineering and Construction Short Subcontract (ECSS) that could be used if the part of the service being subcontracted was primarily construction.
There is also the possibility under both NEC3 and NEC4 to consider the Term Service Short Contract (TSSC) as the basis of the subcontract if the service to be subcontracted is of low risk and complexity. Whichever contract you select, it may need to be added to or amended to capture any flow-down requirements included in your TSC.
If you were to choose to use the NEC4 TSS, you will need to consider changes in terminology and processes in the NEC4 contracts as opposed to the NEC3 contracts. If you were to choose to use an NEC3 TSC as the subcontract, then you will need to consider amendments to this to reflect that it will used a subcontract as opposed to a main contract.