It's to show Weisler's loneliness, and serves as a carry-over in the story.
The movie is set in East Germany, Europe, in the 1980s.
Weisler, a secret agent with outstanding business skills, is assigned to listen in on playwright Dreyman and his girlfriend, Christine. Dreyman is being listened to because of what he says, and he expresses the voice of the people through his writing.
Weissler, who did not report the truth of what he heard during the wiretap, helped Dreyman.
Before the prostitute-calling episode, Dreyman discovers his girlfriend's dysfunctional relationship with a politician, who uses his power to oppress, and Christina, in fear of not being able to be an actress and of hurting her boyfriend, who can't live without the actor's glory and persecution, reluctantly agrees. The plot is roughly like this, a bit long from when I watched it.
Dreiman understood, did not scold his girlfriend and obeyed the request to hold her quietly.
Weissler eavesdropped on all this, he was struck by the fact that, relative to the emotional life of Dreyman and his girlfriend, Weissler lived alone, his home was cold, his work as an agent made him unpopular with the neighbors, he was lonely, and just through the eavesdropping felt a couple of fiery emotions, so he summoned a prostitute, which is to take up.
Weisler bought insufficient time when calling a prostitute and wanted the prostitute to continue, but the prostitute seemed to be in a hurry to catch the next customer. This is a great setup, and it shows loneliness even more when both call prostitutes but don't get enough satisfaction.
After the prostitute call episode Weisler is expectant of the wiretap, he wants to learn about Dreyman and Christina's lives.
Lonely as he is, he is impressed by the couple through the wiretap and feels the warmth of life that makes him a human being and no longer a tool in the hands of politicians.
This allows Weisler to falsely report the wiretap to help Dreyman and Christina, which is enlightening.
For the movie as a whole, the prostitute-calling plot is logical and sensible, which is to say, it serves as an initiation.