Is it okay to do hill repeats right after tempo run?

I have looked up tempo run to see what it refers to.

Hill repeats were Lydiard's way of building speed.

Why? Because speed is power and stride length.

If hills are run properly, one will "bound" up the hill. Springy steps.

Herman Frazier would run "A" mountain when at ASU, and that is a very tough hill to run. Not far, but very taxing. Frazier was an Olympian in the 400m and 4 x 400m relay.

Oregon's Bowerman and Dellinger incorporate hill running, but not as much mileage as the marathoner Lydiard.

So, if you intend to run the hills correctly, and the tempo run drained your energy so that you are quite tired the next day, it may be true that you can't run a hill workout, at least not the way it was intended.

It has a place in your training.

One of the better arguments I've seen for using hills at the end of a run is to force greater recruitment of muscle fibers while tired. When you do a tempo run, or really any strenuous effort, your body will slowly start to "turn off" muscle fibers to protect itself. This can be for a wide range of reasons: fatigue, lowering body temperature, adjusting pH, etc. Basically, what you see at the end of a hard race with runners collapsing is their body selectively shutting off certain things to try to being back equilibrium.

Hills, because they offer additional resistance, will always recruit more muscle fibers than the same rep being done on flat ground (assuming all else is equal). This is just like what you would see with someone doing a back squat with a heavy barbell compared to a body squat.

We tend to be accustomed to letting these fibers trail off as the workout goes as fatigue mounts. Adding hills after is a way to overcompensate and get additional fibers that aren't always called on to "learn" how to work in the later stages of a workout. We would hope that this translates into racing a lot like running a 2 hour long run might teach your body that it needs to maintain a higher quality of movement for longer.

Magness does a good job explaining the idea. This isn't a comprehensive dive into the physiology, but as a model it holds water.

Just understand that there are some limitations to what this session is. You're not building speed, but you're likely promoting someone's ability to kick. Another avenue to consider would be keeping the intensity near tempo effort (as opposed to faster race level efforts) to still get the fiber recruitment you're looking for but not change the aerobic/anaerobic nature of what the tempo was trying to achieve. I've done both, but can't say I have enough real data to say which is better or worse. I usually err on the side of wanting my athletes to feel (or at least look) "fresh" on hills after. If they're grinding it's probably not the session I'm looking for.

If you choose to do this understand how much recovery you need before your next workout and consider if you had enough recovery before attempting this workout.

Would you do a full tempo workout and or a full hill workout?