Advice to replace a discontinued battery
The TR163 is a 3-cell mercury-zinc battery (be sure to take the old one to proper disposal!).   Mercury-Zinc chemistry was favored for equipment design because it had a very flat discharge curve that output about 1.35v (per cell) for most of the service life.

Given the expectation of a flat discharge, you probably want a higher voltage pack and a good low-overhead, low-loss regulator, rather than subjecting the equipment to the substantial voltage variation of today's available chemistries.  

Measuring power consumption using an adjustable power source would be a good first step to sizing.

You will also need to consider usage patterns - for example if this is a memory backup source that needs to be available while sourcing tiny currents you would would need to carefully select a regulator with low quiescent current.  If usage is more intermittent you may be able to use an everyday regulator and put a switch in the circuit, or even only install the replacement cells when the device is to be used.  Noise sensitivity may guide if you can use an efficient switching regulator easily, or if that would require extreme care in filtering.

If you can determine that the equipment will tolerate slight over voltage, NiMH cells might be a crude replacement, but fresh off the charger their voltage can be too high, and they will quickly drop to something closer to 1.2v per cell before somewhat leveling out.

The vintage camera community often faces similar problems with retired battery types; there may be helpful resources there.