Rupert Morrish's answer provides a good alternative. But it's important to understand why "until we talk later time" is incorrect.
"Until we talk later" is a dependent clause. It modifies "take care." In this construction, "until" is a subordinating conjunction which introduces the clause. "We talk" is the subject and main verb of the clause, and "later" is an adverb which modifies "talk." The problem with introducing "time" here is that it does not grammatically fit. "Time" is a noun, but in this construction, "talk" is intransitive. There is simply no room for a noun after it.
On the other hand, "until we talk at a later time" uses a prepositional phrase. In this construction, "later" is an adjective, modifying "time." We then use the preposition "at" to connect it to "talk," which is still intransitive and still cannot take a direct object. The "a" is required because the phrase needs a determiner to indicate which "later time" we are talking about. If we don't want to imply that the "later time" is undetermined, we could consider using a different determiner. However, this really only works in the immediate context of discussing the next time we meet:
"When are we meeting tomorrow?"
"OK. Until we talk at that time, take care."
This is a bit clunky and artificial, but it does work. Note also that we dropped the "later" because the listener already knows it will be at a specific point in the future.
It would also be correct, if very slightly informal, to say "until we talk next time." This is only really allowed because "next time" is a fixed phrase that behaves like an adverb in this context.