In January 2013 Fiji's military regime promulgated new regulations governing the registration of political parties. Among the new provisions was a requirement that all political parties be named in English rather than Fijian. Rather than changing its name, the Soqosoqo Duavata ni Lewenivanua Party wound itself up, reforming as the Social Democratic Liberal Party in order to retain the SDL acronym. However, a subsequent amendment to the Political Parties Decree banned the use of the acronyms of former parties, forcing the party to switch to "SODELPA". The party was provisionally led by Dr Tupeni Baba, but in March 2013 it unanimously selected former SDL Cabinet Minister Ro Teimumu Kepa as its first permanent leader. The party applied for registration on 26 February 2013, and was registered on 3 May 2013.
The party contested the 2014 elections, naming a list of 45 candidates in June. In July, it released its manifesto, promising to reduce poverty, restore the Great Council of Chiefs, and revive the Qoliqoli Bill, which had been stopped by the 2006 coup. The party gained 28.2 percent of the vote and 15 seats in Parliament. Following the election, party leader Teimumu Kepa became Leader of the Opposition. In June 2016, Kepa announced that she was standing down as leader of SODELPA. She was replaced by former Prime Minister Sitiveni Rabuka.
The party ran 51 candidates in the 2018 elections, seven of whom were women. It campaigned on a platform of restoring the 1997 constitution, promising to restore the Great Council of Chiefs within a hundred days if elected, and to consider changing the electoral system to restore communal constituencies. The party won 39.85% of the vote, increasing its number of MPs from 15 to 21.
2020 suspension
On 26 May 2020, the party was suspended for 60 days for breaching the Political Parties Act. All appointees were declared null and void, and were given 60 days to rectify their issues or face deregistration. The registrar stated that the party's Vice President, Vijay Singh, is the only legitimate officeholder in the party. The party's suspension was lifted on 29 June.
