What anesthetic is it? A lot of substances are used in anesthesia: fentanyl and other opioids, midazolam and other benzos. Is it a volatile liquid with a sweetish smell? It could be sevoflurane, an ether with potent anesthetic effects. In any case, if you plan on storing it for more than a year, then I recommend store it in 2 containers: 1 for the main portion that you won't open often, only to take out enough for a few sessions. The first container's cap then should be closed tightly, sealed with
parafilm, and stored in a freezer (sevoflurane's melting point should be below typical freezer temperatures).
This storage method should work for any halogenated solvent anesthetic, and for diethyl ether too.
If you want to draw it into a needle (why? You said it's not for IV, you can't store solutions for IV without a bacteriostatic like benzyl alcohol, and even then it's not meant to be stored for long after first dose taken from it - assume everything that goes in and every time you open it you contaminate it), then you need a special cap that can't be opened, that has a hole with a rubber sheet for needles. Similar to
this, but the one I'm thinking about needs a special device to cap the vial and it can't be opened once capped. When I worked in an analytical chemistry lab, we used those to cap vials of solutions that are air-sensitive and were meant for prolonged storage.