Depends on why it is not taking the grease.
Many times you can cycle / move / actuate what the zerk is greasing and it will then allow it to take grease. For instance my deck lift hardware on the commercial mowers, If someone will actuate the deck up and down, it will accept grease readilly while it will appear "frozen" or clogged if just left stationary.
If you are doing it a lot, there is a tool that goes on the zerk, it is filled with light oil and you tap it with a hammer it injects the oil under pressure.
Many times, I pull the zerk, put it on the grease gun and insure grease passes through (give it a pump) then I dig the old crud out of the hole and then start washing it out with brake cleaner / penetrating oil, whatever is handy and compressed air at times, I usually try and activate the motion that the zerk is trying to lubricate at this time as well.
By this time, I have usually got it accepting grease, but if it still is not working, I will pull the pin or link or whatever (because it only gets worse later) and then clean everything and reassemble.
Obviously, be extremely careful when you activate things (or more so when you have someone else do it) and your hands are in and amongst things that you do not squish or remove something you are attached too.... say a finger or a hand. I have come close several times, but have so far been fortunate.