Usually an incidental opportunity that arises while doing something else, especially in patterns like 〜のついでに and ついでがある.
While I was out shopping, I stopped by the post office.
If you get a chance, please deliver these documents too.
Archaic original sense referring to the order or sequence of things; modern Japanese normally uses 順序 or similar words for this meaning.
In old writing, ついで can refer to the order of things.
Archaic noun use meaning a person who comes next or succeeds someone; not a normal modern standalone use.
In old usage, ついで could also refer to a person who succeeds someone.
While on a business trip, I took the opportunity to stop by my parents' house.
Since it's a good opportunity, I'll go to the post office too.