Can I add an headphone jack to my preamp?

Buy a small headphone amp. You can run it from the tape output, or any other output. Far far easier than adding the electronics internally.
I own four headphone amps. Rudistor, Single Power, Little Dot,and a Tadac.
The Little Dot is about $250 shipped via eBay from China, and was recommended in Stereophile. A nice little tubed job.
The Rudistor mkII is no longer available as far as I know. The Single Power is a 'notorious' headphone amp, (Claims of exploding SP killing it's users are greatly exaggerated LOL.)
The TADAC is a DAC and headphone amp rolled into one.
So for a few bucks to two grand... you can get a nice little headphone amp.

Sure but you need more than the jack; you need a driver for the headphones. Unless you have some experience with adding circuitry an active device, you might best consider buying a stand-alone headphone amp.

Kal