Nope, elephants cannot perform the gait pattern “gallop” as seen in horses, which by definition includes a period of complete suspension (all four feet off the ground at the same time). Source;

https://pubmed.ncbi.nlm.nih.gov/16985198/

The locomotor kinematics of Asian and African elephants: changes with speed and size John R Hutchinson et al. J Exp Biol. 2006 Oct.

Selected quotes:

> We analyzed the locomotor kinematics of over 2400 strides from 14 African and 48 Asian elephant individuals (body mass 116-4632 kg) freely moving over ground at a 17-fold range of speeds, from slow walking at 0.40 m s(-1) to the fastest reliably recorded speed for elephants, 6.8 m s(-1). These data reveal that African and Asian elephants have some subtle differences in how size-independent kinematic parameters change with speed. Although elephants use a lateral sequence footfall pattern, like many other quadrupeds, they maintain this footfall pattern at all speeds, shifting toward a 25% phase offset between limbs (singlefoot) as they increase speed.

> The main difference from most other animals is that elephants never change their footfall pattern to a gait that uses a whole-body aerial phase.