Electrifying a Battery Operated Clock
I have run battery powered  quartz  electric clocks on  mains derived low voltage DC for about 2 decades .They work fine .I made my own low idle current linear regs from garden variety BJTs like BC337 ,BC327 .The battery clock does not need a highly accurate DC voltage because it is designed to keep time as the 1.5 volt cell ages .Now days you could use a LDO P channel reg .I did not use LM317 because the idle current wastes  much more power than the clock .I used a combination of supercaps and electrolytic caps to allow operation during short power outages which are common in my area .Some years later I hooked up a smoke alarm to the system .