I wonder if it is possible to import new tasks about an existing account in
CRM or if I have to delete the account and make a totally new import?

make a totally new import is not gonna make any difference .


Use data migration manager

choose the entity "Task" and map the columns and remember to refer the
"Accountname" on CSV to the Attribute
"regarding" . When you click Next , a screen appears with the name
"Define relationship". check the "Account" and
"Account Name" in drop down .

/Aamir