I've been asked to make an application
you mean that you were hired to create an application, the answer to your question depends on the contract you have with your employer (if you work for a company) or customer (if you are a freelancer).
If you are an employee, generally your employer owns all of the work you produce for them. In this case you do not have the right to release your work by yourself - you must ask your employer for permission.
Your employer may have rules as to what licenses are acceptable for third-party libraries or components. If you work for a well-run company, there would be some kind of a review process before you start working and the issue of GPL should come up there. If you work for a not so well-run company, you may be asked to redo the entire project if your boss finds out you used a GPL library and that is against company policy.
If you are an independent contractor or a freelancer, your contract with your customer should stipulate whether the customer owns all interest in the work you perform. If they do, you can't release the work without their approval because you don't own it. If they don't, you can provide the work to your customer but you retain the ability to also release it yourself under any license you choose that is in compliance with licenses of its component parts, if any.
Important: if your employer or customer expects that you wrote the application from scratch, they do not just expect that you'd spend a certain amount of time on that project (which could be dramatically reduced if you used an existing library, leading to perhaps a lower payment), but also that they would have all rights to the finished product. GPL imposes significant obligations on derived works, and you should probably verify with your employer/customer that it is OK for you to incorporate GPL libraries into an application they are paying you to produce.
I might also have to use a library licensed under Apache v2, but if I understood well that shouldn't be a problem, right?
Apache license tends to not cause issues/concerns because it does not impose requirements that GPL does on the software that uses Apache-licensed components.