Help with airy tone

I play in a large concert band, and have been playing the trombone for a few years now. My conductor moved me up to third chair, and gave me both trombone 1 and 2 parts for all of our pieces. He tells me that the reason it took so long for me to move up, and also the reason why I probably won't move up any further, is that my tone is really airy. He mentions something about "air support." If you're wondering, my lips are not dry, and I have tried really hard just to create a pure sound. Nothing works. I've searched it up a ton, and nothing helps much. I have tried to close my embouchure a little more, but it just ends up sounding pinched and airy at the same time. pls help I might get demoted becuase of this :(