I am not really familiar with the FAA regulation and I didn t renew my FAA ATP since I passed it in a 737.200 in 1995!
For an ATP holder you are showing a lack of knowledge of the rules. An FAA ATP does not expire and there are no provisions to "renew" it. So let's see where you stand. To exercise the privileges of your ATP, you must
1. Hold a current FAA First Class medical. I'm guessing you do not have a current medical but if you can walk and chew gum at the same time that's not much of an issue.
2. You need to have a record of a flight review in the last 24 months from a FAA CFI.
3. To carry passengers, you need to have made and logged three T/Os and landings in the last 90 days in the same category, class and if a type rating is required, type. It does not have to be a "N" aircraft. Again I'm guessing you hold a FAA ATP MEL with a B737 type rating. Any three T/Os and landings, PA-30 through B747 and you're current. To fly the the 737 they would have to be in the 737.
4. To fly IFR you need to have flown and logged, in the last 6 months, 6 approaches, held, and joined and tracked a course in the same category aircraft (special rules for gliders.) Even the Feds admit the last part is stupid because unless all you are doing is ASRs/PARs, every approach will require you to join and track a course. Again, it does not say this has to be done in a "N" aircraft. If you can show approaches and holds from 1995 through 2011, you're current. If not, you'll require an IPC from a CFII in the same category aircraft. Since I'm guessing you don't hold a SEL rating, it'll have to be in a multiengine plane. If you did hold a SEL rating, the IPC could be in a CE-172 and you'd be current.
If your A-330 type was in the last 6 months and you did at least 6 approaches and held during training and have a record of same, you're current in any multi aircraft and all you need is the medical and flight review.