Professors are more established in the scientific community and have most likely already done outreach to some extent.
This means partially that there is more scientific content to build material on and partially that focus might be more on branding of the institution or department in the public media.
Building a strong brand requires knowledge and effort. It does not come over night, but accumulates over time with increasing amount of public exposure. This could be in the form of TV and news paper interviews. Contact with journalists is almost a requirement and if they do not come to you, then you should seek to contact them.
The best thing that can happen for a professor who wants public exposure is a big event in their field of science (major discovery, meteor crash or something of that kind). This will almost naturally attract public attention and then journalists become very interested in an expert opinion. This opinion could come from you – if of course you are an expert.
If your department has a strong public profile in the media, it is more likely that you can build one too. When you do, make sure to align your appearance with the branding strategy of the university. At public talks you can have the university’s logo on a banner or maybe you can bring merchandise or flyers for the audience to pick up and take home. This increases the recognition factor next time you or your department appear in the public space and hence can lead to higher chance of you being the expert next time the news paper wants a scientific opinion.