Area in internet designed to amuse (9)
I believe the answer is:
entertain
'amuse' is the definition.
(thesaurus)
'area in internet designed' is the wordplay.
'area' becomes 'a' (maths abbreviation).
'in' is an insertion indicator.
'designed' indicates anagramming the letters (designed with the letters).
'internet' anagrammed gives 'entertin'.
'a' placed inside 'entertin' is 'ENTERTAIN'.
'to' acts as a link.
(Other definitions for entertain that I've seen before include "Show hospitality to; amuse" , "Put up" , "Act as host" , "Think about" , "Amuse; host" .)