It's hairy, having to carry a deadhead! (5)
I believe the answer is:
beard
'it's hairy having' is the definition.
I can't tell whether this definition defines the answer.
'carry a deadhead' is the wordplay.
'carry' becomes 'bear' (bearing is a kind of carrying).
'a deadhead' becomes 'd' (head letter of 'dead').
'bear'+'d'='BEARD'
'to' acts as a link.
Can you help me to learn more?
(Other definitions for beard that I've seen before include "Goatee, for instance" , "Facial feature" , "Boldly confront (formidable opponent)" , "Whiskers" , "Facial growth" .)