Swear about losing a hairpiece (5)
I believe the answer is:
tress
'a hairpiece' is the definition.
Although both the answer and definition are singular nouns, I can't see how they can define each other.
'swear about losing' is the wordplay.
I cannot really see how this works, but
'about' could be 're' (regarding) and 're' is present in the answer.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for tress that I've seen before include "Rests (anag.)" , "Bit of hair" , "Long lock or plait of hair" , "Switch" , "Obsolete support" .)