Can't a relationship work if?Watch
Well, it depends. Do you have a new girlfriend? If so do you compare your new girlfriend to your old girlfriend? Could you be doing this unconsciously? Does your new girlfriend know you're not over your ex? If you know that the past relationship is over and you won't be seeking to get back together then what you think in your head can be your own secret. You don't have to tell everything. You certainly won't be the only guy to get into a new relationship still thinking about your ex but; if you truly care for the new girl you will forget (hopefully sooner than later) your old girlfriend. If you're not in a new relationship then perhaps its a good idea to give starting over some more time until you're not pining so much for your ex.
So, is your question can you still carry feelings for your ex and have a successful relationship with a current girlfriend? The answer, I suppose, is yes, and you've been proving that for a year, but it's not exactly ideal for the girl who is is just kind of filling the 'girlfriend' role. Is your 'new' girlfriend first in your mind/heart? You're not doing anything wrong you can't help what your heart feels but it's time to be fair to the current girlfriend. What keeps your mind wondering back to the past?
We can all potentially still hold strong feelings for ex's, but it's what we do with them that matters. If we recognize the relationship is over and learn from the experience then after a period of healing by all mean's pursue (or in your case, continue with) relationships with other people. Human beings are complicated and more often than not we don't just forget or stop feeling anything towards someone we once loved. Especially first loves; they tend to be with us the longest and evoke the more stronger of emotions.
Still, if you're actively WANTING your ex girlfriend, maybe even communicating with her and trying to edge closer, then no I don't think the relationship can work. For one thing it's unfair on your partner, it's not healthy behavior, and in the long run it's going to hurt someone.
there are a few factors that will help you decide if this is an issue for you, for example how long has it been since they broke up? if it was a recent(ish) thing then maybe they just need some time to completely get over it which is normal.
If they are acting on these feelings e.g. still messaging their ex often or talking about them too much then this could be a problem. but at the end of the day there will be a reason why they broke up (obviously or they would still be together) and a reason why you are together now.
try not to overthink things, sometimes once you get an idea into your head you overthink it and can make it into a bigger problem than it originally was.
the most important thing is to talk! talk to your boyfriend/girlfriend, let them know if this is really something that concerns you, they wont know its affecting you unless you tell them