If you have used the model contract of employment there is a requirement for the Clerk, if they do not currently hold a relevant qualification, to work towards obtaining one. The latest model provides the option for the Council to specify the qualification required and the date by which it should be obtained, as well as clarifying who should pay the associated costs. This level of detail wasn't included in the previous model, but the commitment to obtain a qualification was. In simple terms, you should do whatever the contract commits you to doing.
Having said that, you should seek to come to an agreement with your Clerk and the other two Councils regarding the apportionment of costs. The cost of the CiLCA is more than just course fees, as you should be paying for study time, travel and accommodation costs if necessary etc.