In case there is a certain level of similarity between your brand name/logo and another already registered/pending trademark, it can cause some issues that can delay and/or prevent your trademark from being registered. All of the owners of similar trademarks have legal grounds to oppose your application on the basis of the confusing similarity between the two marks. Such two marks must, however, be registered in the same country in similar/identical classes of goods and services.
If you wish to minimize the risk of opposition, you can consider changing the similar element(s) of the mark. If this is not a valid option for you and you cannot rebrand, you can still take the risk and proceed with the trademark application. However, the risk that your application might get opposed remains. Should you receive an opposition, you can always hire a legal representative to represent you in the opposition proceedings and negotiate with the 3rd party. However, the outcome cannot be fully predicted.