Commands (including reverse shells, if the necessary binaries/scripts are available) can be launched from Mimikatz using the extracted NTLM hash for authentication. Note that this doesn’t work if your privileges are elevated (weird, right?), hence the initial token::revert command:
token::revert
sekurlsa::pth /user:$TARGET_USER /domain:$TARGET_DOMAIN /ntlm:$TARGET_USER_NTLM_HASH /run:"$FULL_COMMAND_INCLUDING_ARGUMENTS"
The shell produced in this way is a bit weird, as it is actually running as the user that launched Mimikatz (which will show up if you call whoami, though the privileges will be those of the $TARGET_USER.
A number of Linux commands can also take NLTM hashes instead of passwords, such as XFreeRDP, Impacket’s PsExec, and Evil-WinRM.