There are requirements, yes. But it depends on what level you want to compete in. There are two rule books for competitions created by the FN. WBO (Wettbewerbsordnung = Competition Rules) and LPO (Leistungsprüfungsordnung = Performance Test Rules). This is a bit misleading, but in general WBO regulates other competitions than LPO.
LPO: Covers all five levels of competitions (E, A, L, M, S) of showjumping, dressage and eventing. Those are always called “Prüfung” = “Test”. (Hence LPO, for Prüfung).
WBO: Covers “Wettbewerbe” = competitions. This is VERY misleading and by translating it, it gets even worse. In general “Wettbewerbe” are easier than “Prüfungen”.
You get prize money in LPO, not in WBO. WBO is meant to be for beginners, riding school kids, the occasional competition rider and everyone, that just wants to take a look into competing. In addition to being easier WBO has some “fun competitions” which LPO hasn’t cause LPO is the “serious” stuff 
In order to compete in WBO you don’t need much. No test to pass for the rider and no license for the horse, You don’t need to be in a riding club or anything else. Only thing to do is to bring your horse, it’s passport (which IS required) and most organizers require your horse to be vaccined for tetanus and equine flu. So you CAN compete without much effort. But the competitions equal USDF Intro, so it’s nice to do, but if you have any ambition, you won’t be happy there. SJ is no more than 80cm (2’6 or something).
If you wanna take part in LPO you need to to A LOT of things. Horse and rider.
I start with the rider:
0. Be member of a official riding club.
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Needs to pass the test “Basispass” which is a non ridden test where you are asked questions about handling, feeding, nature of the horse, diseases and such general things.
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Needs to pass the test “Reitabzeichen 5” (there a 5 of them in total). This is a ridden test, where you need to do dressage and jumping. Dressage is Level E, so the first Level of the five LPO competition levels, same is with jumping. The dressage test is something like the USDF Training Level Test 3. Jumping is a course of around 8 jumps with 80-85cm so 2’6 - 2’8. You have to get at least a grade of 5 in both of them, so this is about 50% in FEI for comparison. The third part is a theoretical exam (orally) where you have to answer more in depth questions about horses and riding, like explainig the “Skala der Ausbildung”, explain gaits, name tack correctly, describe illnesses and their treatments and so on.
After that you are almost ready to compete. You get “Leistungsklasse 6” (LK6, performance class 6, there are 6, i’ll explain later). Next things to do are:
4. Get your “Competition License”. This is done by sending in the confirmation, that you passed the two tests and paying around 50 €.
This license has to be renewed anually, which is about 30€.
Those licenses get more expensive the higher your LK is.
Horse:
- It has to have an official passport by the FN or the breeding organization.
- Vaccined after strict schedules: Tetanus 1x per year, Equine flu 2x per year, Herpes 1x per year. If the horse lacks this, it’s not allowed to compete.
- It has to be registered as competition horse. This costs 63€ for horses with pedigree. Horses without a proper pedigree (unknown parents, unregistered stallions ect.) cost 152€.
- Again you have to renew this anually which is 22€.
So this is, what you need to compete. But I wrote about the Leistungsklassen (performance levels).
After you passed the test “Reitabzeichen 5” you get LK 6.
This allows you to compete in Level E (first) and Level A* (second), but not in Level L (third) and even not in Level A**.
** is a bit more difficult than , so in sj A is 95cm (3’1) and A** 105cm(3’5) whereas L (no stars here, nobody knows why) is 115cm (3’8).
In order to be able to do A** or L you need LK 5. Which you only get by passing “Reitabzeichen 4”. So again a ridden test, where you have to ride dressage and sj Level A* (dressage is about USDF First Level Test 3). After that you are allowed to do A** and L, but not M (fourth) or S (fifth) level. You can gain the allowance to do so by making further tests (Reitabzeichen 3, Level L test and so on) but you are also able to gain them by results, so wins or placings.
This only applies for english riding. There are NO other english competitions, so you need to do this, if you want to compete in sj, dressage and eventing.
I hope this wasn’t too confusing. It still confuses me. I myself have done both riding tests (5 and 4) and am granted LK 5 to be able to compete in Level A (2nd) and L (3rd).
Few people do this here. It’s considered as a workaround here. Not stating it’s bad at all. It’s just kinda uncommon and trainers would certainly tell you to stop doing it and instead move your hands towards the mouth. But our trainers tend to ridigly follow the books 
So no such things as „little helpers on the way of becoming a better rider“ 
