Jesus began his ministry after John was arrested by Herod Antipas (the ruler of Galilee). There was some overlap between their ministries (John 3:22–24; 4:1–2), but most of the ministry of Jesus happened after John’s.
John belongs mainly to the old order (the time before the full ministry of Jesus; Matthew 11:7–14), while Jesus brings the new. Both men carried out God’s plan, and both were arrested and put to death (Mark 6:14–29; 9:31; 10:33).
Jesus started preaching in Galilee after John's arrest. But John 2:13–4:43 suggests Jesus had an earlier ministry in Judea.