Sorry if this has been asked here somewhere before but I haven't been able to find this question (I found the reverse situation of my question). I've been playing trumpet for several years now and began clarinet a couple days ago for fun. I began to wonder if there could be a backlash with my trumpet playing if I began playing clarinet. Thank you.
I have heard from some of my band directors that the right hand on the clarinet is very similar to the right hand on the trumpet, so this may help with fingerings.
Also the clarinet is a unique instrument because it only produces every other harmonic. Trumpet on the other hand produces each harmonic which is each partial. Although a beginner clarinet play may not be thinking about the partials, they are different and this could be somewhat confusing, but if you don't think about the clarinet in terms of partials at first, you should be fine.
Clarinet requires a firm embouchure while trumpet requires a more loose one. This could also take some adjustment. Your trumpet chops probably wont transfer over to clarinet, but it probably wont be harder than starting from scratch.
Just like any hobby, practicing clarinet will reduce the amount of time you have to practice trumpet. I think as long as you continue to practice both, they shouldn't negatively affect each other, but only increase your knowledge about the musical world.
Playing any instrument is a game of two halves (at least!). There's the music side and the technical side of the instrument. Having played the trumpet, the first skill is well on the way. You can probably read and know what the relationship between notes is, etc.
Trumpet is usually (not always) a Bb instrument. Clarinet is usually (but not always) a Bb instrument. Meaning they are both transposing instruments, and the music is written a tone higher than the pitches actually produced. Whether this is a helping factor will depend on the keys of the pieces you play, but overall, you'll be reading in familiar keys generally.
The embouchure. Very different between the two. With trumpet, you're basically blowing raspberries (so to speak!) whereas with clarinet, there's a reed which needs to be set moving and it's in your mouth. The tonguing is common to both, although that's subtly different.
Fingering has very little in common, pressing valves on trumpet is rather different from covering holes and pressing levers (lots!) on clarinet. Obviously one handed on trumpet compared to needing both sets of fingers on clarinet.
It's all music, but playing both will either take up twice the time, or cost half the time on each. Advantages on trumpet are that you can, with a little effort, also play other brass - same fingering, embouchure, etc., whereas clarinet can be extended to flute and saxes, with similar fingerings and, with saxes, embouchure.
Don't fuss over reading, transposition, fingering etc. The two instruments are similar enough for there to be plenty of transferrable skills. Different enough for trumpet fingering not to be in the slightest confused with clarinet fingering.
The only issue is whether developing a clarinet embouchure will affect the trumpet embouchure. Again, they're different enough that I don't think you've anything to worry about. Go for it!
Playing the clarinet will be easier than if you didn't play the trumpet, but it will still take practice.
Playing the clarinet will not be as hard, as you will already have learnt the music theory. It will also be easier because they both are instruments where you blow! That means quite a few blowing techniques will be passed on to your clarinet playing. Knowing the theory might even help playing the clarinet!
Though the fact that playing it will be easier, there still will be the hard parts. Here is a link that describes some problems normally encountered when picking up a new instrument.