Ground is ground and doesn't differ between sides of the transformer. The arrester is grounded through the shortest possible path. Perhaps you are actually asking which side of the transformer the arrester should be installed on. For that, see my previous response. Without a whole lot more information, the best answer available is "It depends."
I believe that you meant connected when you wrote grounded.
Often the arrestor is located close to the load to be protected.
The impedance of the conductors is typically quite high at the effective frequency of a lightning strike. This impedance helps limit the current and disipate the energy.
With a typical distribution transformer, the lightning protection will be on the primary side of the transformer.
If it is desired to provide protection on the secondary side also, the protector would typically be installed at the panel rather than at the transformer to take advantage of the the impedance of the service conductors.
One pump manufacture markets a surge protector for deep well submersible pumps. These devices are installed in the pump controller at the well head.
Not withstanding the above, check out Cooper Power Systems web site. They have an approach to protecting distribution transformers that I understand includes both primary and secondary protection in the distribution transformer. I don't remember the exact details, check it out.
Normal U.S. practice is to bond the primary and secondary grounds to each other. This is so that as many grounding electrodes as possible work together so as to produce a low resistance connection to ground.
Modern telephone protector blocks under U.S. rules must be bonded to a multigrounded wye primary system that has at least 4 grounds per mile. If local primary distribution is old fashioned 3-wire 3-phase then the building theoretically must have 4 grounding electrodes to make a telephone protector block work.
Overvoltage, possibly from lightning.
Surface tracking.
Failure of the arrestor.
Are we talking about a primary, 13,800 volt arrestor or a secondary surge arrestor installed on the 277/?40 V system?
yours