Is there any importance for URL AGE ?

One of my client he have a domain whcih is example.ae from the last 9 years. Now I have desinged the website for him and need to host the website. But his all social media urls are examplemobile. I have suggested to him we can better purchase the domain examplemobile.com which is availabe for purhcase.

If we boghuth this domain it will effect the SEO ranking.

I heared that old domain have more imporant than newly purhcased domain, Is it true ?

This domian .ae it will icluded in the domain age calculation of SEO Bots.