If the pitcher in question is the one that it arrived with, it had a nice long life. Bid it farewell and sit back and wait for the next one. They come and go and sadly do not stay for a long time.

What conditions are you growing it in? My window neps have no pitchers due to the lack of light in the winter.

What kind of nep is this and how are the growing conditions like?

The pitchers on nepenthes after awhile will dry up and the plant is probably still getting used to it's new home so my guess is that the pitcher that dried up was drying up naturally or it dried up due to the change in it's enviroment so soon the new leaves should start making new pitchers.

Just keep giving it the things it needs and eventually you'll get some nice pitchers.

According to species, your Nepenthes might produce one pitcher at a time, or it might produce a plethora of pitchers constantly. As they adapt to changes in humidity and temperature and light, they will spped up or slow down in pitcher production and might even stop producing pitchers altogether if the conditions are not right. Keep watching the new tendril and see if the pitcher bud continues growing bigger daily. If it swells and lenthens and curls up at the tip it will make a new pitcher and your plant is adapting to your home. If it stays the same size, does not curl, or even dries up and hardens, it has aborted the pitcher and might not happy about something in the environment.

Top up pitchers with rain water when they arrived in the mail to keep them good. Sounds like its not humid enough for it to produce big pitchers and keep them, try it in a hot house, esp.in winter.Maybe not enough light or the wrong growing medium. but most neps are pretty tough with growing medium and quality of water,i'd say not enough humidity.