Calls pig-headed and puts an edge on things (6)
I believe the answer is:
phones
'calls' is the definition.
(I know this)
'puts an edge on things' is the wordplay.
'an edge' says to hollow out the word (remove centre letters) (I've seen 'edging' mean this (edging means the letters on the edges)).
'on' indicates putting letters inside (as in clothing 'on' a person).
'things' becomes 'hone' (I can't explain this - if you can you should believe this answer much more).
'puts' with its middle taken out is 'ps'.
'ps' going around 'hone' is 'PHONES'.
'pig-headed and' is the link.
This may not be correct. Some or all of it may be part of another bit of the clue.
Can you help me to learn more?
(Another definition for phones that I've seen is " 'Calls, rings (6)'".)