Praise be to Allah.
Shaykh Ibn Baz (may Allah have mercy on him) said:
“Clapping during parties is one of the actions of jahiliyyah. The least that can be said about it is that it is makruh (disliked), but the evidence suggests rather that it is haram, because the Muslims are not allowed to resemble the non-Muslims. Allah says describing the non-Muslims of Makkah (interpretation of the meaning):
“Their Salah (prayer) at the House (of Allah, i.e. the Ka‘bah at Makkah) was nothing but whistling and clapping of hands.” [Al-Anfal 8:35]
The Sunnah is, when the believer sees something that he likes or dislikes, to say ‘Subhan Allah (Glory be to Allah)’ or ‘Allahu akbar (Allah is Most Great),’ as was narrated from the Prophet (peace and blessings of Allah be upon him) in many hadiths.
Clapping is prescribed specifically for women if something alarms them during the prayer, or they are praying with the men and the imam makes a mistake in the prayer . In that case, they should draw his attention to that by clapping, whereas men should do so by saying ‘Subhan Allah’, as was narrated in the sahih Sunnah from the Prophet (peace and blessings of Allah be upon him). From this, it may be known that clapping on the part of men implies imitation of non-Muslims and women, and all of that is forbidden. And Allah 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.
“This clapping is not appropriate, and at the very least it is intensely makruh 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 is the Source of strength.” (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 knows best.