The so called religion of peace is very specific on how believers must live their lives. I have said before that it has more prescriptions and proscriptions than I ever thought possible. I am amazed at the level of detail in the rulings on how to live.
Muslims are not permitted to clap. This ruling came from a very informative site. There are quite a few of these sites which offer rulings and interpretations of the koran and sunnahs. If you get the time have a look at these sort of sites they will give you an insight as to what it would be like living under sharia law.
"Clapping during parties is one of the actions of jaahiliyyah. The least that can be said about it is that it is makrooh (disliked), but the evidence suggests rather that it is haraam, because the Muslims are not allowed to resemble the kuffaar. Allah says describing the kuffaar of Makkah (interpretation of the meaning):
“Their Salaah (prayer) at the House (of Allaah, i.e. the Ka‘bah at Makkah) was nothing but whistling and clapping of hands”
[al-Anfaal 8:35] "
The kuffaar (kaffir) is an unbeliever, ie anyone who is not a muslim.