Jagen means to hunt or chase, so it's often called free hunt or free chase, which is far too literal, i.e, a transliteration.
In German fighters are Jager (hunters in one context, or pursuit in another a la early US terminology, which would be verfolgungsjagd)
or even Abfangjager (interceptors), but to translate the actual meaning into its English equivalent means finding the corresponding expression for the same concept (the same expression can be used for the same concept in two languages, sometimes word for word, and sometimes a completely different expression but which means the same thing, which leads to a lot of confusion and mistakes).
The concept of the fighter as a hunter is probably more apt and accurate, as all combat aircraft are indeed Kampfflugzeuge, another generic meaning fight, combat, struggle, that's how it works in German, conceptual generics. This is also one reason why Adlertag was originally very aptly and amusingly set for the Glorious 12th, the opening of the Grouse hunting season in England, and that's where "open season" comes in.