Multiple object tracking faces several challenges that may be alleviated with trajectory information. Knowing the posterior locations of an object helps disambiguating and solving situations such as occlusions, re-identification, and identity switching. In this work, we show that trajectory estimation can become a key factor for tracking, and present TrajE, a trajectory estimator based on recurrent mixture density networks, as a generic module that can be added to existing object trackers. To provide several trajectory hypotheses, our method uses beam search. Also, relying on the same estimated trajectory, we propose to reconstruct a track after an occlusion occurs. We integrate TrajE into two state of the art tracking algorithms, CenterTrack [63] and Tracktor [3]. Their respective performances in the MOTChallenge 2017 test set are boosted 6.3 and 0.3 points in MOTA score, and 1.8 and 3.1 in IDF1, setting a new state of the art for the CenterTrack+TrajE configuration