I have from a very old project a set of icons but I don't have the psd I made. I have 72x72 material design icons like this
Is there a way to properly convert this png icons to higer resolutions?
There are a number of ways to convert bitmaps to vector format, there are online converters but my preference is to use Inkscape and its "Trace Bitmap" tool.
Inkscape is free and (usually) quite effective and will work in most vector formats.
The process would be
File, then Import and import your bitmap to your workspace.
Pathmenu there is the item
Trace Bitmap, select it. You will see a window like the following:
Hopefully after this you should have something vaguely resembling your original image in a vector format. You can use the other Inkscape tools to simplify or otherwise perfect your vector image.
You will then be able to save in whatever format you like at whatever resolution you like.
There is a trace bitmap tutorial on the Inkscape tutorials site
Inscape itself can be freely downloaded from inkscape.org and runs on Windows, Linux & Mac.
I admit this sounds like an advertisement, but I am in no way affiliated with Inkscape. I have just used this tool in the past and found it to be pretty awesome.