Did Shakespeare move the theatre because of plague?

Yes, Shakespeare moved his theatre company, the Lord Chamberlain's Men, several times during the Elizabethan era due to plague outbreaks.

In 1593, the plague caused the closure of London's theatres for eight months. During this time, Shakespeare and his company toured the provinces.

In 1603, the plague returned, forcing the closure of the theatres for a year. Shakespeare moved his company to the rebuilt Globe Theatre, which was located outside the city walls and, therefore, less likely to be affected by the plague.