Amuse American captivated by playing with internet (9)
I believe the answer is:
entertain
'amuse' is the definition.
(I've seen this before)
'american captivated by playing with internet' is the wordplay.
I cannot quite see how this works, but
'american' could be 'a' (common abbreviation - e.g. in organisation names) and 'a' is found within the answer.
'playing' could be 'in' and 'in' is present in the answer.
'internet' could be 'e' (I've seen this in other clues) and 'e' is found in the answer.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for entertain that I've seen before include "Have a mind to - have a party" , "Amuse or take into consideration" , "Think about" , "Provide amusement" , "Have company" .)