About 24-36 hours after treatment I thought it would be best to get a test of my own to have it on my NHS record. I gave a urine sample for a NAAT PCR test and it returned negative result. I assumed this meant I had treated it successfully or I never had it. 

Unfortunately yesterday the symptoms of white discharge in the morning returned. I am considering further testing, but my query is as follows:

Can cefixime and azithromycin suppress Gonorrhea in a NAAT PCR test but not cure? ( My understanding on PCR is it would still pick up dead bacteria so my negative was a true negative either through treatment or not having it?)

Would you advise wider testing as the Gonorrhea should be cured and other infections are more likely since I was PCR NAAT negative?

NAAT tests for gonorrhea and chlamydia !are amongst the most accurate tests in all of Medicine and your negative result is strong evidence that you never had gonorrhea or chlamydia.  If you did, treatment with cefixime and azithromycin would cure over 98% of Gonorrhea.  The small amount of discharge that you have noticed may have been the normal urethral secretions that most men experience from time to time, but which are noticeable only if a person is looking hard for them. These secretions are most notable first thing in the morning and are noticed intermittently, whereas abnormal penile discharge due to STI‘s tends to be continuous. Alternatively, you may have a discharge due to Mycoplasma genitalium or non-chlamydia – non-gonococcal urethritis. Tests for M. Genitlium are widely available in the UK.  If you test for him. Genitalium and have a negative test you can be confident that the discharge you have noticed is not due to an STI and does not represent a threat to partners.

My suspicion is that what you were noticing is a small amount of normal urethral secretions. EWH.