Разгадате шараду. my first is a principal man in any school but without a head. my second is a little part of something. my whole is what you can see in any art gallery.

My first is a principal man in any school but without a head. - headmaster (директор школы)
My second is a little part of something. - piece (кусок)
My whole is what you can see in any art gallery. - master+piece=masterpiece (шедевр, произведение искусства)