Applauding at first, children laugh when entertained by funny magician (10)

'applauding' is the definition.
(acclaiming is a kind of applauding)

'first children laugh when entertained by funny magician' is the wordplay.
'first' suggests taking the first letters.
'when entertained by' is an insertion indicator.
'funny' is an anagram indicator.
The initial letters of 'children laugh' is 'cl'.
'magician' is an anagram of 'acaiming'.
'cl' inserted within 'acaiming' is 'ACCLAIMING'.

'at' is the link.