In my my 1 bedroom condo I have an electrical panel 100 AMP photo below, I'm looking to install a 240V dryer plug. I currently have a washer dryer in one combo that runs on a 120V outlet with water hook up already installed. I just wanted to know if this is possible as I would like to eventually switch to a separate washer, and ventless dryer which runs on a 240V outlet.
The good news: you could move breaker 11 to 1 or 9 and then put a double breaker in 10/11.
The bad news: these panels have a very bad reputation. See https://inspectapedia.com/fpe/Federal_Pioneer_Panel_Safety.php and Federal Pioneer panel safety for some details. It is a good idea to get a reputable electrician to check the panel and possibly replace it.
FYI, here is how your panel is phased (behind the curtain). Notice how 240V breakers are positioned so half is on each phase. Your 30A/240V dryer breaker will need the same.
Remember you must use /3+ground cable to a dryer. Using /2+ground is not allowed, because dryers need neutral, and the exemption that once allowed bootlegging ground off neutral has been gone for decades.