I think that the consideration was already made via the original agreement. The variation is a change to the original. So, in my opinion consideration has already been made. This relates to my experience in English Law only.

In some jurisdictions (such as England and Wales) a contract requires 'consideration' (in addition to offer, acceptance and intention).

A variation of a contract is itself a contract - that is, an agreement to vary the original contract. Therefore, a variation will require consideration.

However, it may not be essential to expressly refer to 'consideration'. Consideration is an exchange of promises of value. When parties agree to vary a contract, the consideration can be found with both parties promising to carry on performing the contract as varied.

Having said that, if there is ever any doubt whatsoever as to the presence of consideration, it is always preferable to state clearly what the consideration is. Or (in English law) you could execute the document as a deed.

In the wording of your example, not only the price to be paid for the variation is set but also the terms and conditions or description of the variation is set: 'in accordance with the arrangements set out in this Variation Agreement'. In this case, I understand it as an option to choose: either the original contract, either the modified terms and conditions which works with a different price.
You may offer a variation without any additional cost any time the change to consider does not impact the resources, time or cost of the considered project; or whenever the parties have planned a variation mechanism or tolerance and already included it in the initial price and defined the scope of such authorized variation.

Thanks a lot Graham,Michael and Anne for sharing your inputs on this topic.

Best Regards,
Anirban