Production of Succinic Acid from Crude Glycerol using Fermentation
Glycerol has 3 carbon atoms and succinic acid has 4. So you need (apart from some redox reactions) a way to add another carbon atom.

Also, succinic acid appears in the citric acid cycle. What you have to research are anaplerotic reactions. When you remove any of the metabolites (like succinic acid) from the cycle, you have to replenish them. One way is to turn pyruvate (3 carbons) into oxaloacetate (4 carbons), as shown in the wikipedia article on anaplerotic reactions:

$$\ce{pyruvate + HCO3− + ATP -&gt; oxaloacetate + ADP + P_i + H2O}$$

Then, you have to find a pathway from glycerol to pyruvate. Here is a schematic of glycerol metabolism:



Source: https://www.researchgate.net/publication/224950286_Effect_of_impurities_in_biodiesel-derived_waste_glycerol_on_the_performance_and_feasibility_of_biotechnological_processes/figures?lo=1

As you can see, it is possible to turn glycerol into pyruvate fairly directly (using reactions of glycolysis). 

To put everything together, you just need an organism that secretes succinic acid, and make sure that these pathways are turned on sufficiently that most of the provided glycerol gets metabolized to succinic acid. As this involved oxidation, the organism has to have access to oxygen or some other oxidation agent.

UPDATE

Prompted by Andrew's comment, I found a paper where they optimize succinate production from glucose. As you can see from the scheme above, glycerol can be funneled into glycolysis by two enzymes (using one ATP for phosphorylation and one NAD+ for oxidation). The enzymes used for the remainder of the reaction (and to provide NADPH via the pentosephosphate pathway) are shown in the figure from the paper below. You would need to provide some glucose to feed in the pentosephosphate pathway to have sufficient NADPH, or invoke some other pathways:



Source: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4983090/figure/Fig1/?report=objectonly