Need new converter or special hose?
You need a quick connector at the compressor... it looks something like this:



The things to get right are whether the threaded end is male or female, the size of the threads (1/4 NPT is common in the US, but YMMV), and the compatibility with the connector you already have (if you don't feel like changing it as well). I can't really tell, but it might be a type M connector. Just to make things more complicated, there are different sizes out there.

If it was me, I'd unscrew the connector from the compressor and bring everything to a store that stocks such things to put it all together. In the US, any big box Home Depot/Lowes/Menards would have that.