英語を使う部署に異動する可能性がありますって英語でなんて言うの？

"I need to study English.." When you talk about the need to study English or the need to do something it means that you are doing it because it is required or it will bring other opportunities your way.

"If I study....." When you use this phrase you know that "if" you do something it could bring a possibility of something happening in the future. This means you want to take the chance to do this so the possibility of something good can happen in the future.

It depends how much information you wish to share about this topic how much you say. You could respond very briefly:
"I need English for my work," or give a much longer explanation detailing your hope that someone within your company will one day put your name forward for transferring to a department within the company where English may be needed.

I study English' and 'I am studying English' are both the same and both grammatically correct. We then use 'because' before we are going to give the reason. We could also use 'might' or 'may' in this sentence, to show that the reason is a possibility but it is not certain. Then using 'transferred to a department' means that within your company you are being moved to a different job but still in that company. And finally, 'that requires me to use English' you could also say ' that I will need to use English for' in more simple English.

When you are moved from one department to another then this is called 'transferred' If you can read/write and speak English in your work this is also called 'using' or to 'use' English

In order to explain that the reasoning behind learning English is the possibility of a new job that requires using English, you could say, "It is possible I will be transferred to a job where I would need to use English". This sentence highlights the reasons for wanting to learn English.