When you say, "adding new application at existing oracle 11gr2 database", you you literally mean new schemas in an existing database, or do you mean a new instance on the same machine that is used for another database?
If you mean in an existing instance, then you have to ask what objects it expect to use outside the main schema. If it requires public database links and public synonyms, it probably isn't going to sit well with other applications.
Apart from that, my main issues will be about the impact of the new application on the existing applications. Will it affect performance? How big is it? Do you have enough size? What impact will the dependencies have on backup and recovery?
It's kinda difficult to know exactly what to say because the question is so vague. I know nothing of your existing application, or the new one, so I'm not really in a position to comment.
PS. A word of advice. It's never a good idea to say things like, "at your earliest possible time" or things like urgent. It suggests that your time is more important than everyone else's, so it sounds rude. If you want a service level agreement you need to pay for support. If you ask questions on a free format, you can't make demands.