Playing in time and in tune
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You won’t last long if you can’t play in time and in tune. Although there is certain relativity here, depending on how well the rhythm section lays down the time and the pitch.
You say “pitch” in the rhythm section? Yes the core pitch of the ensemble comes from the keys and bass. I learned from an old time trombonist that listening to the bass for pitch and the high hat and snare for time would usually serve me well.

Back to relativity: Some bands don’t care about pitch - time and feel are the essence. I’ve played on some like this and while it can be annoying, and put the hurt on your chops, all in all I’d rather have it feel good than be perfectly in tune. Although it’s a shame.

When you’re playing lead, you are the king of the horns, but when you and the drums don’t settle on where the beat is, the kingdom is in disarray. The Hi-hat often plays eighth notes, and the sub-division makes it a great source for listening. The kick drum and the bass should work as a unit and when you are focused in, and in the “zone” you can ride along with them quite easily.

Different eras begat differing styles of playing. In the 30’s it was all quite square triplets, and much more of a 1 and 3 feel. Moving into hardcore swing, the feel was 2 and 4 and the triplets loosened up a bit. Phrasing relaxed and wasn’t so Ricky Ticky. I suggest you listen to all the styles of the name performers on good recordings. Be prepared to know what goes where and  how long and how short the accents are.

When I was a teenager I sat in my room and played into a reel-to-reel tape player while listening to a metronome and a constant pitch on an old electric cord organ. I played the same exercises over and over at different tempos, and developed the ability to hear  96 BPM or 120 BPM in my mind the same way I could hear a concert A or a Trumpet Bb or F#. With these relative landmarks I became a great sight-reader.

Maurice Andre was my favorite sound. I used to play along with him in my headphones until I could match his vibrato and slight embellishments on pitch. He had a neat way of raising the 3rd’s that made his scale unique and quite French.

When you play you need to lightly tap your feet. Left on 1 and right on 2. This creates hetero-lateral rhythm and is much more stable than homo-lateral rhythm. We are bipeds and if you think about it, it’s pretty hard to walk out of time☺

Lock in the feet with the drums and you’re good to go.

Perhaps the biggest area of confusion is where the brass section should play on the beat. Some times it’s right on the money – kind of and English approach to time. Then there’s slightly on top of the beat, that’s some old stride jazz or newer pop. Then of course there’s the laid back approach. But it can be way back like Basie or slightly back like Miller. Whatever the feel – the lead trumpet sets the example. Whatever approach you take, make it musical, and never confuse the band as to whether you are playing dotted eights or triplets. Be precise and above all be consistent.