it basically just means bring with the implication being that they would then also administer it. The down is probably only used because the anesthetic is stored on an upper level in the facility. Having said that the sentence is worded a bit strangely.

It means that there is some anaesthetic somewhere (probablemente upstairs(arriba)) and that they will bring it to use on them if they do not be quiet. Una persona tiene que estar silencoso. Pero el no esta silencioso. anaesthetic es una droga q te hace dormir. El va a darlo la droga para hacer el silencioso Si no estas silencioso voy a darte este droga y vas a dormir - si estas dormiendo.. estas silencioso