Hello,
If a message says "your account has been disabled in the App Store and iTunes Store" or "You cannot login because your account has been locked", you might be able to request reactivation by tapping Continue right from the alert. If that does not work, Apple provides a link with three options for this specific issue. Tap or click here ➞ https://getsupport.apple.com/?caller=kbase&PGF=PGF63005&category_id=SC0245&symptom_id=23362 .
or for additional telephone contacts refer to: Contact Apple for support and service - Apple Support
Apple does not say how long it takes and I have never needed to have this service done. My impression is it does not take long unless you need help from a real person and you have to wait for a business day. There are new, self-service features.