Hi!
Gitblit uses log4j version 1.2.17. This version is not affected by Log4Shell.
To reach the same exploit effect with log4j 1.x a specific custom logging configuration is needed, making use of JMSAppender. Gitblit does not do this in its default configuration.
Thus, Gitblit is not affected by Log4Shell.
If you had altered the logging configuration of your installation in an exploitable way, then you would need to fix that. Otherwise you are okay. You should make sure, though, that your installation is protected against others writing or adding configuration files.
Here some links with background information, why we say that Gitblit is not affected.