to that extent is an adverb meaning "to the degree or extent that". It carries one recorded sense.
to the degree or extent that
“insofar as it can be ascertained, the horse lung is comparable to that of man”
“so far as it is reasonably practical he should practice restraint”
Definitions, synonyms and semantic relations for to that extent come from Princeton University’s WordNet. Commonness is measured against a corpus of everyday English. Full sources and licences.