Hi,
I assume that you are an EU-citizen. In this case the rules about EU social security coodination apply to you.
The rules say that you must only be insured against unemployment in one country at a time, and that country should be where you physically perform your job. So, in your case you should keep membership in the danish A-kasse.
Its not relevant where the employer is based – its where you physically perform the job, which is important.
If you will work less than 25% of the time in Denmark, it will be the rules about working in two EU-countries at the same time, which will apply to you. However it does not seem to be the case for you.
You can read more about EU Social Security Coordination in our article here:
https://www.a-kasser.dk/eu-social-security-coordination/
Let me know if you have further questions.
Best regards,
Anders Weber, A-kasser.dk