Newer wireless card work with older router?

So I was wondering if older router like 5 year old technicolour could have any issue working with wireless card like tp link wdn4800?
I have heard that newer rputers need newer cards but is opposite true just confusing.

No it shouldn't in terms of connecting. Because the settings in the card should set the correct settings to be backwards compatible with the older router. However, you will be limited in the sense that you are using an older router with older standards that may not suffice for current needs.

tldr; will it work? yes. Will it be great? probably no.

Your going to be limited by the speed of your old router, but it will work.

Yes

The specification sheet for the wdn4800 says it supports the four wireless standards 802.11 n/g/b/a which is pretty much all of the used ones in consumer wireless devices, except ac.

If you want to learn more, have a look at this wiki explaining the different standards of 802.11.