I have been fumbling about in GA since the previous administrator retired without passing on passwords and other insights. We have had a UA code on our website for quite a while. Is there any way I can create a new account and use the same UA code or do I need to start completely over and have our web developers/host update the UA code?
If you remember the UA code then no need to create one again, if you don't remember UA code then simply create one. If you need any help about google analytics or Search Console or if you need to do SEO audit for your website pm me, its free
If he can grant you full access on your email then you don't need to create one and you can keep on using the same which I guess is not an option for you but I still mentioned it as sometimes IT guys don't want to share passwords as they have other websites on the same account. Otherwise you will need to create a new account and create a new code.
I will suggest you to get rid from the previous UA as quickly as possible. Create a new Google account if you don't have any and then create a new GA code and put it on website so you can check analytics instead of someone else