I would not recommend trying to get a sear on shrimp that are already fully-cooked. This will almost surely result in severe overcooking and tough, rubbery shrimp. I'd just find a method to gently heat them though (such as tossing in a sauce in a pan for a couple minutes) and serve after minimal handling, as they are already cooked.

Throw th cooked shrimp into some marinara sauce, simmer few minutes and pour over pasta.

Being that I never trust the sanitary handling of already cooked shrimp or any shellfish I always give them a quick dip in hot water then back into ice water. Pierino's suggestion into the pasta water would work great. I would consider doing this to help thaw. A pan sear I too would worry about over cooking. BUt if you have to maybe do while partially thawed to help from cooking the center at all. Just a thought.

I'm not sure if this would 100% work but if I had to sear cooked shrimp, here's what I'd do:

1. Keeping them cold (but defrosted)
2. Making sure they're dry
3. Searing quickly on a really hot cast iron skillet with a little oil with a high smoking point such as canola, clarified butter or sunflower oil (not butter and extra virgin olive oil etc)

Still a chance of overcooking and it probably wouldn't beat raw shrimp though.

I am sorry to say that I wouldn't advise trying to sear already cooked shrimp. It will surely be overcooked! I live on the Gulf Coast and cook a lot of shrimp and fish. Perhaps you could modify the dish and just use it at room temp along with the rest of your hot ingredients.

Frozen shell on or shell off? If it's already cooked I'm guessing the latter. The main thing here is be sure they're completely defrosted. As in completely. Dry the shrimp in towels, and when you are satisfied with dry then crank up a pan with hot oil or butter or combination of both and sear quickly. Of course you could also just blanche them in the pasta water for a minute or so, drain, and toss all together. That would be a no sear but at least the shrimp would be cooked.