how long will it take for a store of tritium to become safe?

Answer 1

half life of tritium is 12.32years

In our lab , we believ that a time of 10 half-life corresponding of a decay of 1/1024approximately 10^-3 was sufficient

So, it would be 12.32*10= 123.2 years

But your question was incomplete. You should precise the contamination

Answer 2

The Half life is around 12.3 years, so I would say no earlier than 24 years. 36 would be a much safer bet.