There is a Fatwah of Shaykh Ibn Baz about clapping, which states that: “Clapping during parties is one of the actions of Jahiliyyah (ignorance). The least that can be said about it is that it is Makrooh (disliked), but the evidence rather suggests that it is Haram, because Muslims are not allowed to resemble the Kuffar (disbelievers).”
Allah (swt) says, describing the Kuffar of Makkah (interpretation of the meaning):
“Their Salat (prayer) at the House (of Allah, i.e. the Kabah at Makkah) was nothing but whistling and clapping of hands.” (Al-Anfal 8:35)
When the believer sees something that he likes or dislikes, the Sunnah is to say ‘Subhan’Allah (Glory be to Allah)’ or ‘Allahu Akbar (Allah is Most Great),’ as was narrated by the Prophet (sa) in many Ahadeeth.
Clapping is prescribed specifically for women, if something alarms them during the prayer, or they are praying with men and the Imam makes a mistake in the prayer. In that case, they should draw his attention to the mistake by clapping, whereas men should do so by saying ‘Subhan’Allah’, as was narrated in the Saheeh Sunnah of the Prophet (sa). From this it may be concluded that clapping on the part of men implies imitation of Kaafirs and women and all of that is forbidden. And Allah (swt) is the source of strength.
The Standing Committee was asked about men clapping, when they play with children, or children clapping to encourage their classmates. They replied: “This clapping is not appropriate, and at the very least, it is intensely Makrooh, because this is one of the characteristics of the Jahiliyyah and because it is something that is done only by women to draw attention to a mistake in the prayer. And Allah (swt) is the source of strength.” (From Fatawa Islamiyyah, vol. 4, p. 332-333)
Children can be encouraged by saying ‘Allahu Akbar’, if they do something that the watcher or listener likes, or one may use other suitable phrases or raise one’s hands, or raise one’s voice in words of praise, such as “Well done!” or “Excellent!” and so on. And Allah (swt) is the source of strength.
(Source: Islam Q&A – Sheikh Muhammad Salih Al-Munajjid)