WordNet sense 1 (a person who backs a politician or a team etc.):

admirer, champion, friend, protagonist, supporter

WordNet sense 2 (a thief who steals goods that are in a store):

lifter, shoplifter

WordNet sense 3 (someone who is an active supporter and advocate):

promoter, plugger

WordNet sense 4 (an amplifier for restoring the strength of a transmitted signal):

booster amplifier, booster station, relay link, relay station, relay transmitter

WordNet sense 5 (the first stage of a multistage rocket):

booster rocket, booster unit, takeoff booster, takeoff rocket

WordNet sense 6 (an additional dose that makes sure the first dose was effective):

booster dose, booster shot, recall dose