This claim is true to a certain degree. To begin with, the author of the article, George Chidi, is a legitimate writer for the Guardian and has written for them for over a year. In addition, the source is from The Guardian, which leans left-center but is mixed on factual reporting. However, in this article, there were multiple links to sources, in all of the claims the author makes in the article.
The claim that Elon Musk could use his new department for self-gain is factual. I found another Newsweek article that also brought up the former Federal Communication Communication Direction Blair Levin. This article also backs up the claim that Elon Musk stands to benefit from his new role in the forthcoming Trump administration. Elon Musk is a big critic of the Broadband Equity, Access, and Deployment (Bead) Program, and if the Trump administration guts that program he stands to benefit from it.
To conclude the claim is true, however, it should be pointed out that right is a hypothetical situation that could occur. There is no evidence right now that Elon Musk is using his new department because Trump has not been inaugurated yet.
Links
George Chidi Linkedin
The Guardian Bias
Newsweek
Elon Musk's Tweet