The possibility of Government job is your horoscope is there, however it can also be in semi govt , bank, insurance etc. The period is strong after June 2016. However you should remember that your Sade Satti is going on and therefore things will not be easy. You will have to work very hard to get the desired results on this front.
10th house which is the karmabhav or the house of career / profession is ruled by Jupiter. Jupiter or Guru as we know it is for knowledge and related to teaching, sharing of knowledge. Jupiter is posited in the 6th house which is for competition and aspects the 10th house, therefore Yes the chances of Job in the teaching sector is very much in your horoscope and you would excel in it. Keep working hard and you will see lot of growth in your career.