Yes. Chromatically. It’s a Glissando.

 

I wouldn’t necesssarily play it chromatically. You could get away with putting an F# and E in there, then underblow to ‘ghost’ those notes while dropping the pitch with your embouchure. When you hit the C# then push the air again. Listen to Cannonball for how he often drops down to notes like that.

 

Emphasize the first note and last note, with a lightly breathed chromatic in between.

 

If it's European Art Music, play it chromatically. Conductors can be pretty picky.
If it's any sort of popular music, fake it with a gliss. No one will know the difference.

 

I'm with Jamie. A 2 note gliss is fine in this case.

To speed up your playing. Play it slow, perfectly, then gradually increase speed. There are no shortcuts. If you do take a shortcut, it's going to be sloppy. Ultimately try to play along with the recording to match the phrasing, accents, articulation, rhythm and style.

 

Any tips to speed my playing up? I'm a slow player, and I don't have enough time

If you don't have more time, then your only alternative is to practice more efficiently. Many people waste much of the time on their horn. Determine what needs attention and then focus. Putting in hours of practice is meaningless if you don't gain something from it.