Nice secure run and coop.
The easiest thing that comes to my mind,,,,,, is adding your addition to the far end outward. I am judging from viewing, that your run is about 8 feet x 8 feet. (not counting the portion under coop. Extend same amount into the grass portion on the far end with Chain link fence. 4 foot high. Then secure the top with welded wire stretched across. You will end up with a secure portion of run,,, just not covered with overhead roof. Make a close-able gate into new run portion on one corner of your existing run structure. Maybe 3 foot wide, by 4 foot high. Open and close access to new area as you desire. During fowl weather,, chickens can choose not to venture to open area on their own. You can still get inside the 4 foot portion,, although bent over to 4 foot height.
Another option that is quite simple is to make your addition with cattle panels. They are 54 inches wide by 16 feet. The pix below looks like it is a 2 panel structure.
With the base 8 feet wide, you would be able to walk more comfortably inside. I suggest adding the welded wire or hardware cloth on top of hoop, for security from predators.
You could add a top tarp onto above,,,, but do have to consider winter snow load. There are ways to add additional interior support to deal with that as well.
WISHING YOU BEST,,,,,,,,,,,,,,,,,,,,,,,,,,,,and
