Because you have a new stick with a newer serial number on it the Disney+ App rollout might be done in batches based on the box / stick serial number.
I would imagine it will be there within 24 to 48 hours if you only bought the stick recently.
I have the same problem as @Cookoospite
Downloaded the Disney plus app yesterday but when launching it says it needs a update from sky, checked for system updates and it says its upto date last updated march 7th
I am using the black now TV box 4201sk
Any help appreciated thanks
I am guessing you tried removing the Disney + App from your My Apps section, then carry out a fresh App install from your device Apps Store ?
Other than that try a forced up date in the hidden menu by following the instructions below (update the software even if you are on the same version number).
This updates your software, fixing any faults in the process.
Fast Forward x3