Damaged Solder Joint?
The hole may still contain part of the leg that was originally soldered there. In addition, because the hole is attached to a plane you will need significant heat in your soldering iron to keep the solder hot enough to properly melt into a sufficient fluid to soak it up with wick.

Try heating it again with a little bit of fresh solder that contains flux till it melts all the way through, then with a suitably thin piece of single strand wire, poke it through the hole till while keeping the heat on till it clears whatever is still in the hole. Then keep pushing, or pull the wire through the hole. The wire should eventually take the remaining solder with it.

It is important the tip is hot enough and large enough to have a decent contact area. If your tip is too small, or you are too aggressive and apply too much force you will just auger out the pad which is bad.

If the board is double sided, drilling through is an option, but if it is multi-layer I would advise against this, especially if the pad connects to the inner layers or planes.

Once you clear the hole, install the new part and carefully solder from both sides then check the connections with your ohm-meter. If need be add a jumper wire to the nearest good trace or plane. You may need to scrape off some etch resist with a knife to do so.

ADDITION: Since that looks like a tandem connection, i.e. both go to the same place, if one is damaged electrically (e.g pad on one side only) you may get away with using it without rework, though mechanically it will be weaker.