Many thanks for your patience. I must advise you from the start that there is no definitive right or wrong answer here. Both options are possible - that the agreement had ended and was no longer applicable and that it had carried over to the new assignment. I have seen similar scenarios end in both possible outcomes.
There are arguments for both to be honest. What may not necessarily help you is the fact that this was the same client, through the same consultancy, doing the same work. Unless there was a practice of agreeing entirely separate/different contracts each time someone was placed there, the chances are that the same agreement would have been used, therefore implying that it was carried over this time.
On the other hand, you can also argue that you simply do not have anything in writing to prevent you from moving there and that the only document that you have dealing with this was for a previous assignment, which has now ended.
What is certain is that the consultancy can challenge you in court over this, if they really wanted to. In the end it would be for the court to decide whether they have a valid claim or not and this will always be fact-specific based on the individual circumstances. There is no way to avoid this. I would hope that the consultancy would actually not go as far as court, and they will only ask you or threaten you not to do this, but without ever claiming. You could consider taking the risk, but if it looks like they are going to claim, you can reconsider your position and perhaps decide to delay the work just to be on the safe side.
I trust this has answered your query. Please take a second to leave a positive rating by selecting 3, 4 or 5 stars above - this is an important part of our process and recognises the time I have spent assisting you. If you still need me to clarify anything else, please reply on here and I will assist as best as I can. Thank you