Hi, thanks for your question. My name's XXXXX XXXXX I'm going to assist you with it.
Broadly, as long as the terms of a contract do not require any variations to be in writing, parties can amend the contract orally.
For such amendment to be effective there has to be a binding agreement to the variation by both parties (i.e. it needs more than one party simply providing notice of the change to the other and both must agree to it). Directors have ostensible authority to bind the company they are appointed to, so where variation is permissible, a director can make a binding amendment even if that director is different to the one that signed on behalf of the company in the original agreement.
However, there also has to be some sort of "consideration" for the change. Consideration means something in return for the contractual promise or, in the case of a variation, something in return for the amendment to the contractual promise. Consideration can include a mutual abandonment of rights or new benefits being granted. A verbal concession by one party to change their contractual rights will not constitute a variation and, in the absence of consideration, would need to be effected by a written deed.
So, in short, a verbal agreement to change a written contract can be made by directors of the repective parties but there would need to be consideration for the change and the contract would need to be examined to ensure it does not include a provision prohibiting variations other than in writing.
I hope that's helpful. Can I clarify anything for you?