trophy hunting

Short definition from Wiktionary

Noun

1. 1
   The killing of a carefully selected animal, particularly big game, under or without government license to acquire a part of the animal, such as the head or skin, as a souvenir.
2. 2
   Alternative form of trophy hunting.

Verb

1. 1
   present participle and gerund of trophy hunt
2. 2
   present participle and gerund of trophy-hunt