Hi all. how can i remove old app icon in launcher? old app icon that was removed a long time ago

Let me rephrase your question: you removed an application and the icon for this application still shows in the launcher, is this correct?
Did you restart the desktop since that removal?
You can also try to purge the application (depending a lot on your distribution, so can't tell you in detail how to do that without more information)

FWIW: when it comes to KDE applications, the icons are part of the KDE icon set, I don't advise to remove that manually

FWIW2: you can of course edit the residual entry in the launcher by right-clicking -> Edit applications and remove the entry if it really still exists after a log out