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By Justin Melvin
Answer: MEDICAL EMERGENCY

Each of the provided clues is a phonetic reinterpretation of the name of a medical condition that may require urgent care.

Clue Phonetic interpretation Medical condition
Butt repair for the singer of 1000 Forms of Fear ASS FIX SIA ASPHYXIA
A cylinder for Poirot, oh daughter of my parent TUBE HERCULE OH SIS TUBERCULOSIS
Woman on Goats Head Soup must pay Murphy, Mom ANGIE OWE EDDIE, MA ANGIOEDEMA
The Kid’s home for birds on a cliff to contact on the phone - yuck! BILLY AERIE CALL ICK BILIARY COLIC
Probe clock sound? You will tempt a ripped front of a leg TEST TICK YOU’LL LURE TORE SHIN TESTICULAR TORSION
A bunch of press about a solemn promise for an ancient city (Farrow) HYPE OATH UR MIA HYPOTHERMIA
Palin’s note in a place for iniquity, running or racing SARAH TONE IN SIN DROME SEROTONIN SYNDROME
Overturn a place for a building, Sierra UPEND A SITE ESS APPENDICITIS
Going the direction opposite kata, saturate the directional line ANA FILL AXIS ANAPHYLAXIS
A dorsal cup of chai for non-fake guys: The Little Ninja (the Aphex Twin alias) BACK TEA REAL MEN NINJAI TUSS BACTERIAL MENINGITIS
Regarding zero, it does not count as success RE: NULL FAILURE RENAL FAILURE
An old, male red deer, a stud HART A TACK HEART ATTACK
Butler in the old South, dissolve a separate squadron RHETT ANNUL DETACHMENT RETINAL DETACHMENT
From the Spanish, creepy, err… DEL EERIE UM DELIRIUM
An Azadirachta indica for Rosemary’s portrayer AN NEEM MIA ANEMIA
Dwell location MULL AREA MALARIA
A pirate’s bird, a chevalier: you and me together PARROT A KNIGHT US PERITONITIS
Wildebeest groan about Long from Fresh Prince GNU MOAN NIA PNEUMONIA
The tendency to ask invasive questions about the skyward direction PRY UP -ISM PRIAPISM
Jeff Smith comic injects liquid in the ground to get oil and deodorant brand BONE FRACK SURE BONE FRACTURE
Colorant to encourage criminal activity in a city south of Seattle DYE ABET TACOMA DIABETIC COMA
The top part of a grain plant in Father Ted’s curse? Eschew! EAR IN FECK SHUN EAR INFECTION
The Quercus that belongs to me makes an automobile end a Hardy girl MY OAK CAR DIE TESS MYOCARDITIS
Vampire hunter and Jekyll’s worse half meet a beam to climb up quickly by gripping with arms and legs D HYDE RAY SHIN DEHYDRATION
A musician like the Ramones agrees casually to a 1991 compilation album by Autopsia PUNK SURE WOUND PUNCTURE WOUND

Reading the boxed letters in order gives the clue phrase PLEASE STATE THE NATURE OF THE. Some searching reveals that this is a frequent catchphrase of the Emergency Medical Hologram from Star Trek: Voyager. The answer is the completion of the quote, PLEASE STATE THE NATURE OF THE MEDICAL EMERGENCY.