Am I eligible to apply for courses other than my specialisation subject for universities abroad?

Can I apply for courses other than my specialisation for universities abroad? Is it even possible?

My qualifications: I have completed my bachelors in economics but now I want to apply for masters in Development Studies or International Politics.

Yes it is very much possible to transition into a new subject for your masters degree and universities do accept applications for the same, however, some universities expect applicants to demonstrate a strong foundation in their chosen field.
If your undergraduate degree is not directly related, you’ll need to bridge the gap through relevant coursework, certifications, or other means.