This sentence seems to be talking about a government which has two political parties. You would talk about your colleagues on YOUR side and your colleagues on the OTHER side. For example, in the United States, our government has two main parties: Republicans and Democrats. If you are a Republican, you would refer to the Democrats as your colleagues on the other side. So, in your sentence, "on the other side" could be deleted, but it would change the meaning slightly. Instead of the speaker specifically referring to his colleagues on the other side, he would mean ALL of his colleagues, the ones on his side and the ones on the other side. So I would really ask the chairman and my colleagues on the other side, let's get the answers. Especially referring to the colleagues on the other side. So I would really ask the chairman and my colleagues, let's get the answers. Referring to ALL his colleagues, on both sides.

In parliaments there are 'two sides' the AYE side and the NAY side. they sit on opposite sides of the room, on the right is the Government, on the left the Opposition. In your case, the 'Chairman' would be head of the AYE side. But in a board meeting there should be no 'sides', they are supposed to work together, not to oppose each other. 老鬼