Advancement to Likert Scale Likert Scale has been widely in use for more than 80 years (it was published in 1932). However, the limitations of it are well-known:


The space between each choice is possibly not equidistant. 
People keep endorsing the mid-point of the scale and avoid choosing the “extremes" options on the scale, even if an extreme choice would be the most accurate.
Attitudes of the population for one particular item in reality exist on a vast, multi-dimensional continuum. However, the Likert Scale is uni-dimensional and only gives 5-7 options of choice
Peoples’ answers will be influenced by previous questions


What is the latest development in Psychometrics? Is there any budding and promising replacement or advancement for Likert Scale?
The visual analogue scale (VAS) has been used in some research. For a direct comparison in one study, see Vickers who compared VAS vs. 7-point Likert.

It's interesting that Vicker found a similar effect to that found in a highly cited paper by Dawes on 5/7-point Likert vs 10-point Likert, namely that more points on the scale result in a lower average score... despite the fact that the stuff measured in these two studies was completely different: muscle soreness and respectively customer satisfaction. Well, the probability of this coincidence is 50%, but I couldn't find any meta-analysis of this type of study.

One additional issue with Likert (and other ordinal) scales is that some researchers use the wrong statistics on it, like those assuming normal distribution, c.f. Bishop and Herron, who also discuss some finer points.

Refs (spelled out):


AJ Vickers, Comparison of an ordinal and a continuous outcome measure of muscle soreness,  Int J Technology Assess Health Care. 1999;15(04):709–716
J Dawes, "Do data characteristics change according to the number of scale points used? An experiment using 5-point, 7-point and 10-point scales", Int J Market Res. 2008;51(1)
PA Bishop and RL Herron, Use and Misuse of the Likert Item Responses and Other Ordinal Measures, Int J Exerc Sci. 2015; 8(3): 297–302.