MLAs spent 45 minutes paying tribute to their former colleague as Stormont resumed following the Easter break. The sitting was also suspended for half an hour as a mark of respect.
The Ulster Unionist Party deselected Mr McClarty after a row in the local party.
Local UUP councillor Norman Hillis then inadvertently recorded a phone call onto Mr McClarty’s voicemail in which he described the sitting MLA as “a spent force”, “toast” and “burnt-out”.
Although hurt by the deselection, Mr McClarty stood as an independent and trounced the two UUP candidates, neither of whom was elected.
Speaking at Stormont last Monday, Mr Nesbitt said: “What happened to David McClarty then should not have happened. To his family and friends who were so badly hurt by those events, I am glad to take this opportunity to publicly say sorry.”
Mr Nesbitt also paid tribute to Deputy First Minister Martin McGuinness’s decision to attend the MLA’s funeral: “In the spirit of building a shared future, I wish to acknowledge the presence of the Deputy First Minister at the funeral last week.
“I know that many surprised themselves by going out of their way to make sure that Martin McGuinness felt welcome, as many did for me when I attended Clonard monastery for the requiem Mass for Father Alec Reid, it might indeed be a fitting tribute to David McClarty’s memory that we start showing the same respect to one another in life as we do in death.”
Assembly Speaker Willie Hay said that the late MLA had served his constituency well and said the tributes “reflect the high esteem with which he was held in this house”.
DUP MLA Gregory Campbell said: “He was a very difficult man to dislike because of his gentlemanly way of dealing with people.”
Mr McGuinness said that Mr McClarty was “an absolute gentleman” and added that although he was “a unionist to his backbone but highly respectful of all traditions in our society - he was always very fair”.
SDLP leader Alasdair McDonnell said that the Coleraine representative had “presented his robust unionist position in a most civilised, tolerant and openly inclusive way”.
Alliance leader David Ford said he was “a friend and a colleague to all of us here”.
NI21 leader Basil McCrea said that he had attempted to get Mr McClarty to join the new party but he had refused out of a principled desire to remain independent.
TUV leader Jim Allister said that Mr McClarty “certainly was a gentleman in how he conducted himself” and that “the resilient way in which he bore his illness was a mark of the man”.
Green Party leader Steven Agnew said that Mr McClarty had “always maintained personal relationships in the face of disagreement”.
UKIP’s David McNarry said: “I think that he did know, colleagues, how popular he was with us all.”
Claire Sugden will take over David’s seat at Stormont.