‘After these things there was a feast of the Jews, and Jesus went up to Jerusalem.'
Some time later Jesus went up to Jerusalem for ‘a feast of the Jews' The manuscript evidence strongly favours no definite article. We do not know which feast it was. What the author could not remember he did not invent. It is clear from this that Jesus made a practise of attending the regular feasts, as the Old Testament had commanded, even though with the dispersion of the Jews the practise had become less widespread due to problems of distance and of travel. John is still concentrating His attention on Jerusalem and Judea.
‘After these things'. A vague time note which could cover any length of time. Its purpose is to connect the narrative with its context and to indicate a new subject. It is not in order to give us specific information. It need not indicate chronological sequence, but simply a change of subject.