The service is free for developers who make fewer than 3,000 API calls per month and paid access starts at £50 per month for up to 15,000 API calls. according to https://techcrunch.com/2012/08/30/cambridge-university-press-launches-an-api-for-its-dictionaries/ which is posted 7 yrs ago.
However, it needs to request for an key now from https://dictionary-api.cambridge.org/apply