At the base level that would depend on the biology of the species. Individuals of most species are physically capable of mating with more than one mate in a lifestime. So purely monogamous species (one mate in a lifetime) are going to be more rare. Serial monogamy is also common. More than one mate, but still only one mate at a time. Polygamy, more than one mate at the same time, occurs in some species as well.
However is it going to be very rare for a monogamous species to have polygamous matings. While polygamous species could have monogamous mating.
Mate selection involves physical biology so these attributes can be used to help determine the mating system. For example gorillas are polygynous (more than one female per male) so gorilla males are huge to defending their mates. While gorilla females are smaller.
Angler fish are polyandrous with multiple smaller males attaching to the female, eventually becoming little more than an appendage.
In humans males, on average, tend to be slightly larger than females. At face value this looks like slight polygynous leanings. Although humans have similar size differential with Bonobos that have a very loose mating system. Like them, we are capable of monogamy and polygamy(polygyny and polyandry). Our tendency is to seek out multiple mates in our lifestimes, even when in existing relationships.
As for Klingons since they are human actors in makeup the would carry the same bonobo-like size differential indicative a similar mating system with humans.
https://en.wikipedia.org/wiki/Monogamy_in_animals
Klingons raised in the empire appear to be a generally scummy lot.
Which saying nothing about non-monogamous mating systems.