This is a container anagram - look for an indicator word that suggests mixing letters, plus another word that indicates one thing going around or containing another.
"Unusually" is the anagram indicator - rearrange the letters of ENERGETIC. "Around" indicates this anagram should contain the middle letter of the word "day".
Answer: GREAT-NIECE | "Unusually" indicates an anagram of ENERGETIC, which goes "around" (contains) the middle letter of dAy, which is A. Anagram of ENERGETIC containing A = GREAT-NIECE.