As an English name it has been in use since the Middle Ages, originally in the form Clare, though the Latinate spelling Clara overtook it in the 19th century and became very popular. It declined through most of the 20th century (being eclipsed by the French form Claire in English-speaking countries), though it has since recovered somewhat.
Already growing in popularity due to Australian model Elle Macpherson (1964-), this name received a boost in the United States after the release of the 2001 movie Legally Blonde featuring the main character Elle Woods. In the United Kingdom the name was already fairly common at the time the movie came out, and it actually started declining there shortly afterwards. A famous bearer is American actress Elle Fanning (1998-).
This is not the usual spelling in any of the Scandinavian languages (in Sweden and Denmark it is Freja and in Norway it is Frøja) but it is the common spelling of the goddess's name in English. In the 2000s it became popular in Britain.