You can't do this only with
chmod. You can, however, make a new group and change the group ownership of the directory, add the user to that group and then give the group the permissions you want on the directory, so you can give privilege to only that group.
To create a group
tomcat and add the user
tomcat8 to it:
sudo groupadd tomcat && sudo adduser tomcat8 tomcat
You may also want to add yourself (and any other users who need read write access here) to the group with
sudo adduser [username] tomcat
Now change the group ownership of the directory:
sudo chown :tomcat /usr/local/javaagent/appagent/ver2/logs/Tomcat1
Don't forget the colon - this is to change only the group ownership.
Now change permissions, for example, you add read and write permissions to the group like this:
sudo chmod g+rw /usr/local/javaagent/appagent/ver2/logs/Tomcat1
From your question I'm not sure what you want the other settings to be. I recommend reading
man chmod and this guide to permissions to understand better what you are doing.
Directories need execute permissions to be entered and searchable, so you most likely want octal
775 (so all users can read and search but only group can write) or
770 (so only owner and group have any permissions - keeping the directory private)
-R as it's unlikely you want all files to have execute permission.
You probably do want to add the setgid bit though, so that files created here by all users inherit the same group ownership as the directory:
chmod g+s /usr/local/javaagent/appagent/ver2/logs/Tomcat1
Or using octal, in one step:
chmod 2775 /usr/local/javaagent/appagent/ver2/logs/Tomcat1
which gives these permissions:
s in that position is the setgid bit) or
chmod 2770 /usr/local/javaagent/appagent/ver2/logs/Tomcat1
To check permissions and owners on the directory, use
ls -ld /usr/local/javaagent/appagent/ver2/logs/Tomcat1