The most common and most likely answer to this crossword clue is the 6 letter word PERUKE
P
E
R
U
K
E
More clues leading to the result PERUKE
Buddy explains!

The straight part
We know that "Covering for hea" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case covering for hea = peruke.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does PERUKE mean?
PERUKE noun- A wig, especially one with long hair on the sides and back, worn mainly by men in the 17th and 18th centuries.