Hagrid keeps his broken wand. Breaking seems a mode of punishment and not just an inconvenience.
Can a wizard buy a new wand if the old one is broken?
Hagrid keeps his broken wand. Breaking seems a mode of punishment and not just an inconvenience.
Can a wizard buy a new wand if the old one is broken?
It fully depends on the reasoning behind the breaking of the wand. Upon accidental breaking of the wand, a replacement can indeed be ordered. However Hagrid had his wand broken as a punishment for being expelled from Hogwarts. He is not allowed to practice magic as he never graduated.
I should also mention that he keeps his broken wand inside his umbrella and still uses magic.
Mentions of broken wands being replaced that I can remember are:
Neville Longbottom, he got a new wand after breaking his dad's old wand.
Ron breaks his wand on the whomping willow in CoS and gets a replacement by the PoA.
Why not? Ron got Charlie's old wand when he started at Hogwarts. One or 2 other examples are available. I expect wizards in good standing can purchase a new wand.
Ron bought a new wand with the remainder of the Weasley's windfall after they visit Egypt in the Prisoner of Azkaban.
Wizards can get new wands if theirs is broken, damaged, or worn out, even if they previously had bought a wand that chose them. Ron gets his brother Charlie’s old wand, so presumably Charlie was able to buy a new wand easily enough.
“You never get anything new, either, with five brothers. I’ve got Bill’s old robes, Charlie’s old wand and Percy’s old rat.’
Ron reached inside his jacket and pulled out a fat grey rat, which was asleep.”
- Harry Potter and the Philosopher's Stone, Chapter 6 (The Journey from Platform Nine and Three-Quarters)
Charlie’s wand is not in a particularly good condition when Ron gets it, so it’s likely the reason he needs a new wand is because his old one is too worn to work as well as he’d need it to.
“He rummaged around in his trunk and pulled out a very battered-looking wand. It was chipped in places and something white was glinting at the end.
‘Unicorn hair’s nearly poking out. Anyway –”
- Harry Potter and the Philosopher's Stone, Chapter 6 (The Journey from Platform Nine and Three-Quarters)
When Charlie visited the Burrow, he has a wand, so he was indeed able to get a replacement wand. Also, Ron couldn’t have given back his old wand because Ron accidentally breaks it in his second year.
“The source of the commotion was revealed as they entered the garden and saw that Bill and Charlie both had their wands out, and were making two battered old tables fly high above the lawn, smashing into each other, each attempting to knock the other’s out of the air.”
- Harry Potter and the Goblet of Fire, Chapter 5 (Weasleys’ Wizarding Wheezes)
Additionally, after breaking Charlie’s old wand Ron later buys a new wand, though that is the first wand he has bought.