Umrah visas are not issued after Ramadan. Pilgrims who go to visit during Ramadan must leave the country when Ramadan ends and cannot overstay this time. Basically, you have to leave on Eid or shortly after Eid.
Visas are not issued to people for Umrah after Ramadan so there is no way for you to go then. The only people who can perform Umrah after Ramadan are GCC nationals; those with permanent residency or work permits and Saudis. This is as I mentioned above in order to control the flow and make sure they are ready for Hajj. If you want to go for Umrah after Ramadan you will actually have to wait after Hajj.
In short Visas for Umrah are open approximately 9 months out of the 12th, this is minus the preparing period and Hajj time.
If you want more practicalities with regards to Umrah then make sure to sign up and receive the Umrah transportation guide. Also do join my newsletter as I share information and deals there.