Can I create an Automator application to start Tomcat when I need? I can start Apache Tomcat (installed via HomeBrew) in Terminal using

$ catalina run


But it does not work in an Automator application Shell script using bash 

I tried to set up a bash Shell script in Automator like this: 

catalina run


When I run the Automator application, it won't work and shows -: catalina: command not found. 

What is the correct way to create an Automator application, or do I need to use AppleScript?
When you run a shell command or script in Automator it is passed your system's default PATH, not the one in your bash profile. This is why bash cannot find the catalina command.

You should always specify the full path to the command in shell scripts. If it was installed via HomeBrew this is probably /usr/local/bin/catalina but you can confirm this by running which catalina in a terminal session.