Can I change old burglar alarm panel for new (honeywell optima compact gen4 panel) without sounding the alarm?

Disconnect the battery or sounder in the bell box.

The external alarm sounds because you have removed the power source from the panel. This is to enable the sounder to activate if any potential burglar tries to cut the power to the property. If you don't have ladders long enough to reach the external bell as with Kevin's' answer. To keep the noise to a minimum you could power the external bell directly from the panel battery whilst you replace the rest. Then once mains power is initiated connect the bell wire to the panel.

It depends on the bell and how its activated, some bells will sound if certain connections are removed not just the power connections, given that this system has probably been in some time the bell box is unlikely to have that feature. depending on the bell box you may be able to place that into a hold off mode before disconnecting it from the panel, otherwise as suggested above should minimise the noise, it will help if you have the engineers code/ or user codes to hand as opening the main panel could cause a tamper alarm that needs silencing this can usually be avoided if the panel is put into engineering mode first.

Unless you manually climb up to the external sounder using ladders and disconnected the power supply in the sounder, the sounder should turn off after 15-20 minutes. External sounder has to turn off after a period of time due to environmental reasons. A lot of systems are 15 minutes by default unless reprogrammed by an engineer.

The alarm sounder automatically will turn on when the mains are cut from the panel. If the sounder has its own battery you need to disconnect it after opening the lid. When changing the panel you should get help from an experienced installer.