active

Performed started giving regular concerts
I still think what is meant here is "reqular" or "busy".


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Note added at 4 hrs (2019-05-25 14:38:22 GMT)
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Sorry typo:
PerformeR

"At this time, X began giving frequent concerts."

In your context, did this activity last for some period of time and then stop or slow down? Or, does it mean until the end of his life / until the present time? If the former, then you could add "a period of" and write:
"At this time, X began a period of intense concertizing."
FWIW, I guess "concertizing" is used more frequently for classical musicians or even folk music or some popular singers, than in the rock music world. Also, does the Russian original imply touring? One can do heavy "concertizing" but remain in one city or even one theater.

If it's the latter case - that the performer began this activity at the time mentioned and is still doing it to this day or did it to the end of his life, then I'd go with "began giving frequent concerts," because "intense concertizing" sounds specific to a delimited period of time.

"intense concertizing" (NB - Examples are almost all with "years of" or "a decade of," etc.
https://www.google.com/search?tbm=bks&q="intense concertizin...

One can also attach "intense" to the period of time, rather than to the activity itself.
"an intense period of"
https://www.google.com/search?tbm=bks&q="an intense period o...

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Note added at 8 hrs (2019-05-25 18:08:59 GMT)
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Reply to Sofi: As I said, "a period of" suggests that it began and then it ended, and that the text will now go on to tell about what the person did after this period of intense concertizing. It's not a strict requirement, but in your case where the activity continues up until now, I would use some formulation with "giving frequent concerts." Or, if you want to bring in the element of this happening in various countries (even though it's not in the Russian), you could use a variation on rns's version with "touring," and write "... began an intense schedule of international concert tours" or something like that.

"The trio began an intense schedule of touring the world, playing up to 80 concerts a year..."
https://www.smallslive.com/artists/1205-shai-maestro/

As for "that time" vs. "this time," either one is OK in the past tense. Which one feels more appropriate depends on the context - how much detail is given about the circumstances, etc. Without being able to give you a fully reasoned or strict explanation, I would tend to use "this" if the particular time period is more thoroughly described, as opposed to the author linking the event with, say, just one other event. Examples - again, this is not a fixed rule (sentences composed by me; don't try to look them up):

"After the war she moved to New York City and began to look for a job in publishing. She worked as a copy-girl at Women's Wear Daily, carrying sheets from the AP ticker to editors at their desks. She lived in a one-room apartment on the West Side. This was when she began to study medieval literature in depth, staying up late into the night to read by the single dim lamp in her room."

"His wife left him soon after he returned from the war. That was when he decided to become a serious scholar."