Took part, according to the account by Edward (5)
I believe the answer is:
acted
'took part' is the definition.
(as in an actor taking a part in a production)
'the account by edward' is the wordplay.
'the' becomes 't' (the is pronounced as a 't' sound in some dialects).
'account' becomes 'ac' (abbreviation for account).
'by' means one lot of letters go next to another.
'edward' becomes 'Ed' (short for Edward).
't' after 'ac' is 'act'.
'act'+'ed'='ACTED'
'according to' is the link.
(Other definitions for acted that I've seen before include "Performed (in a play)" , "Behaved or played a part" , "did something!" , "produced an effect" , "Took part in play" .)