I am facing a scenario under Option A NEC3 contract where the PM requested a quotation under clause 61.2. for additional work.
The contractor submitted his quotation which the PM assessed but to a lesser amount than that which the contractor quoted.
I assume the contractor now has to carry out the additional work and if he disputes the assessment he must follow the dispute resolution route.
In simple terms yes. A clause 61.2 quotation is for a proposed instruction, to which the PM can either say they do not wish to proceed or to instruct them to go ahead. At the point of this initial quote being requested for the Contractor is not proceeding with that work.
PM once they get the quote can then decide if they wish to say no they do not wish to proceed, or if they do indeed wish to instruct them to now proceed with these works. If they did not agree with the quotation they can still instruct them to proceed, and then still make their own assessment (in accordance with the contract). The Contractor will have the dispute process to follow if they wish to challenge it.
Once the work has been instructed to go ahead with (which would be after they submitted the quote) at that point they would have to proceed with the works.