Jesus is in Galilee speaking to his brothers. These verses tell about when this event occurred. (See: rc://en/ta/man/translate/writing-background)
After these things
These words tell the reader that the writer will begin talking about a new event. "After he finished speaking with the disciples" (See: John 6:66-71) or "Some time later"
the Jews were seeking to kill him
Here "the Jews" is a synecdoche for "the Jewish leaders." AT: "the Jewish leaders were making plans to kill him" (See: rc://en/ta/man/translate/figs-synecdoche)
Now the Jewish Festival of Shelters was near
"Now the time for the festival of the Jews was near" or "Now it was almost time for the Jewish festival of Shelters"