Sir Jeffrey won the seat in Lagan Valley – the constituency he represents at Westminster – just days ago after contesting the Assembly election.
The Electoral Office of Northern Ireland confirmed on Thursday that Ms Little-Pengelly had been returned as an MLA for Lagan Valley.
Sir Jeffrey said his party will not nominate ministers for the Stormont Executive until the UK Government takes action on the protocol.
In a statement, he said: “The people of Lagan Valley and throughout Northern Ireland gave me a mandate, based on a commitment that we will not nominate ministers to a new Northern Ireland Executive until the issues flowing from the Northern Ireland Protocol are satisfactorily dealt with and Stormont is able to return on a stable and durable basis.
“I will continue as the Member of Parliament for Lagan Valley until the protocol issues are resolved.
“It is important that the protocol is replaced with new arrangements that respect Northern Ireland’s place within the United Kingdom and as the leader of Unionism that work is in London.
“In the interim period, I have asked Emma Little Pengelly to represent people in the Lagan Valley constituency at the Northern Ireland Assembly.
“Emma will be a first-class advocate for people and will work hard to advance the issues that matter to everyone in Lagan Valley.”
Ms Little Pengelly said her party leader has an “important task to complete in addressing the continued problem of the protocol”.
“This requires him to be in London and working closely with the UK Government,” she said.
“Consequently, I have agreed to fill his seat in Lagan Valley, at this time, both to support this work and to ensure a continued high level of support and service to the constituents of Lagan Valley.
“It is a privilege to be asked to fulfil this role at this important time for Unionism and for Northern Ireland.
“While Sir Jeffrey focuses on that immediate task, I look forward to serving the people of Lagan Valley with passion and commitment.”
Unionists strongly oppose the post-Brexit trading arrangements as a border in the Irish Sea.
The Northern Ireland Assembly is due to sit on Friday for the first time since historic election results saw Sinn Fein become the first nationalist or republican party to top the poll.
The first order of business will be the nomination of a new speaker, without which the Assembly cannot sit.
Earlier this week, Sir Jeffrey did not rule out his party refusing to nominate a speaker.
On Thursday, he said the party will decide on Friday whether to nominate for the position.
Ms Little Pengelly previously served the party as a senior special adviser and was elected as MP for South Belfast from 2015-17 before losing the seat to the SDLP’s Claire Hanna.
She has most recently been working as a barrister in Belfast.