ASE 16 Tested a sequence that works.
1. Need to use "create or replace" option to update trigger in place.
2. Login who wants to re-create the trigger need to take the ownership by alter modify owner command
e.g. alter table dbo.Table1 modify owner loginame only TestLogin2
This basically changes the ownership of Table1 and triggers on it from old login to your new login
This is maintained in sysobjects.loginame column.
dbo privileges are sufficient. sa/sso not needed.
3. Then run the "create or replace" SQL to change the trigger in place.
HTH
Avinash
See the attachment for exact sequence I followed.