Headless: Remove the first letter of a word
"Shot epic without leader (3)" gives PIC
Tailless: Remove the last letter of a word
"They clipped article (3)" gives THE
Heartless: Remove the middle letter(s) of a word
"House lacks core pipe (4)" gives HOSE
Wingless: Remove the outer letters of a word
"Estate rejects outsiders immediately (4)" gives STAT
This puzzle also features compound clues, which include more than one wordplay device.