It's up to your ISP to assign you a new public IP. Unless you have static IP, there is a chance you'll get assigned a different one by restating your modem, but that's the best you can do.
Have you tried contacting whoever manages the services your IP appears to be blocked from?
this.
the point is when the ISP assigns you a seat. it is keeping you assigned to that seat.
but as most of us encounter, we frequently come across WiFi setups that keep you assigned to that way way too long.
and you can't get it to renew. if you close your notebook. whatever. it will still keep you assigned to the original location. and you can't get it or force it to assign you a new location. you are locked into using a given ID and password of course.
happens to me most frequently when traveling in Asia, many times at hotel wifi.
even if i tell them that their lease time is far too long they don't get it.
wifi admin and the IT service contractors have set up in a way that doesn't meet the reality for how users actually need to use it in their location.
rebooting doesn't get you a new location.
connecting to a different network temporarily usually doesn't work.
what does usually work is if they can give you a different ID and password and connect with that, and then shifting back to your former ID/password usually does force a change.
what also is annoying is that apple's software and many WIFi initial login screens don't play well together. and trying to force a log in screen to pop up again (after an initial sign in and connection) is sometimes problematical even if you disconnect. getting that login prompt back again just sometimes will not worK even if you temporarily disconnect from the network.