There’s no right or wrong methodology for determining when to introduce cardio training in your fitness program. It pretty much depends on your personal goal. For example, if you’re a competitive bodybuilder, you’ll want to do more cardio. Typically that means on the same day you train usually at the end of your routine.
From the phrasing of your question, it would seem like you’d like to balance the gains you’ve made against losing some fat. If that’s the case, I would add cardio work gradually, keeping in mind there’s no “rule” as to how many times per week you need to perform it. Performing a minimum of 20 minutes per session with the goal of steadily increasing the intensity should get you started. You can do that by adding more cardio sessions, or, increasing the amount of time you do cardio. Either way, you’ll need to pay close attention to your caloric and sleep requirements to insure you are still fueling your training and muscle growth.
As for pros and cons, adding cardio will require more time at the gym. Increasing your training volume by doing cardio on the same day you train may require more recovery time than just doing the weights. You could add more training days if you do cardio on the “off” days. But, that would require more of your time. For my goals, I’d prefer to do cardio on the same day as my training. But, that’s not to say that I don’t occasionally switch the cardio to an “off” day. And, as I stated above, you’ll need to pay closer attention to your nutrition to avoid a calorie deficit. On the plus side, balancing cardio with your weight training, will provide you with the opportunity to reveal the muscle tissue you’ve worked hard to attain. And, adding cardio will certainly benefit your overall health as well.