It's no secret that tennis thrives when there are great rivalries at the top of the game. While Serena has had stretches where she's struggled with injuries or a loss of interest, she hasn't had a true rival on the WTA Tour for nearly a decade. Everyone acknowledges Serena's greatness, but there comes a point where people grow tired of any one person's dominance.
If Federer had maintained his 2003-2006 dominance for five-ten more years, some may have continued to marvel at his greatness. However, many more would have tired of seeing him win all the time. Having Nadal and Djokovic around made Federer more compelling, and through no fault of her own great rivalries is something Serena's career (and accordingly the last decade of the WTA Tour) largely lacked.
The WTA Tour has some potential rivalries that could develop in the next few years, and would really benefit if they come to fruition. The worst thing that could happen post-Serena is a period where majors are won by random players who are rarely heard from again. However, this seems unlikely given that there are plenty of talented players waiting in the wings. It also doesn't appear like any of the younger stars are going to come close to approaching Serena's singular dominance, so there's a chance some serious rivalries begin to emerge.
Eugenie Bouchard versus Simona Halep would be easy to promote, and is the most natural emerging rivalry. It's got the natural contrasts, players of similar ages, and lots of talent. Both are already solid top ten players, but it remains to be seen if they can separate from the pack. It's not too late for Wozniacki and Ivanovic to get back to the top, but it seems unlikely they'll start regularly challenging for majors. Sharapova is still only 27, so it's not too late for her to develop a brief rivalry with someone over the next few years if another player reaches her level.
American fans will be hoping Sloane Stephens, Madison Keys, Lauren Davis and Christina McHale can jump to the next level, and if so tennis in the US would be in good hands for years to come. However, for rivalries amongst this group to really gain traction beyond serious tennis fans they'll all need to rise fairly significantly in the rankings.
Regardless of who it may be, the WTA Tour would really benefit from one or two strong rivalries at the top of the game. It's something that's been missing for too long in a sport that's had some great ones over the years. It's not realistic to expect another Navratilova vs. Evert, but it's not too much to hope for a rivalry that can grasp fans' interest for the next several years.