When Circuits merge you will need to tell the archivists in the repositories you are using, and they will close the series which contain the old circuit(s). Wherever you decide to deposit the records of the new Circuit, they will set up a new series.
In some cases, if all the old circuits were in the same local authority, you will continue to use the same record office. If the new circuit crosses local authority boundaries, and the different churches within it used to deposit their material in different places, the Circuit Meeting will have to make a decision. The current arrangements are that we go by where the "head' church of the Circuit is. That is usually the place named in the Circuit name. Fine if you are in the Loughborough Circuit, but less so if your circuit is Hants-Surrey Border, for example, or even Bede!
The important thing is that you deposit the records somewhere, and inform the Liaison Officer for Methodist Archives (email: archives@methodistchurch.org.uk) who will be happy to offer further guidance on the most sensible option.