Constant dripping of urine is called urinary incontinence, meaning Apollo cannot control his urination properly. There are many causes of urinary incontinence, and it will be important for your veterinarian to sort out what is going on specifically in Apollo's case.
Urinary incontinence can develop secondary to urinary tract infection and inflammation, which is simple to diagnose and treat (in most cases).
In male dogs, particularly neutered male dogs, urinary incontinence can develop due to hormonal imbalance resulting in weakness of the urinary sphincter muscle (this muscle tightens around the urethra to hold urine inside). If this is the cause of urine dribbling, treatment is relatively easy and effective using oral medications to improve sphincter tone.
Urinary incontinence can also be seen secondary to neurologic disease in which the nerves that control the urinary bladder are not functioning correctly and the bladder cannot empty appropriately. The urinary bladder remains large and flaccid and results in what is called overflow incontinence (meaning the bladder is so full that it must spill out to avoid popping like a balloon).
A less likely cause of urinary incontinence in Apollo's case would be a developmental abnormality in which the tubes that connect the kidneys to the urinary bladder develop in the wrong place and therefore the urethral sphincter can't hold urine in appropriately. This is less likely since he is 6 years old and just recently developed a problem (usually these dogs are incontinent their whole lives).
Lastly (and perhaps most importantly) urine dribbling can be seen in cases where bladder stones are present and are causing a blockage of the urethra. In male dogs prostatic disease can also cause urinary blockage. Signs of urethral blockage include straining to urinate but nothing or very little comes out, general discomfort and anxiety, frequent posturing, and frequent licking of the penis. Urinary blockage can become a life threatening emergency if the urinary bladder ruptures as a result of the increased pressure. If Apollo is posturing to urinate and is unable to produce a stream of urine, he needs to go to the emergency clinic ASAP to be evaluated.
If Apollo is able to produce a normal stream when he tries to pee, he should still be evaluated by his regular veterinarian sometime this week to determine the underlying cause of his urine dribbling. They will likely recommend abdominal x-rays and blood and urine tests (could be a simple urinary tract infection).
I hope this answers your question. Please let me know if you have any further questions or need any clarifications.