On 7 December 1964, when the former Lord High Chancellor Reginald Manningham-Buller was created Viscount Dilhorne, of Greens Norton in the County of Northampton. He had originally been elevated to the peerage two years prior, as Baron Dilhorne, of Towcester in the County of Northampton, for his appointment to the Lord Chancellorship. This was also one of the last times a hereditary peerage was created.
This seems excluded by the wording of the question, but there are more recent examples of peers advancing to a higher rank by inheritance.
Among the hereditary peerage, Francis Grosvenor originally became a peer in 1957 when he succeeded his father as Baron Ebury, of Ebury Manor in the County of Middlesex. Then in 1999, he became also Earl of Wilton when the previous earl, a distant cousin, died childless. The 1st Baron Ebury was the younger brother of the 2nd Earl of Wilton; the 1st Earl being their maternal grandfather.
Life peerages are all created at the rank of barons, but some has been given to heirs of higher ranked hereditary peerages. The latest example seems to be Robert Gascoyne-Cecil, a former Conservative Leader of the House of Lords. He was created Baron Gascoyne-Cecil, of Essendon in the County of Rutland, in 1999. Then on 11 July 2003, he succeeded his father as Marquess of Salisbury.
Note this is distinct from inheritances by heirs who bore courtesy titles: the practice where children of high ranking peers with subsidiary titles, uses one of the lesser titles "by courtesy". This carries no legal validity - the parent retains the actual title - and thus do not confer membership in the peerage. However, there used to be a rare legal device called the writ in acceleration, which "accelerates" the heir of a peer to the House of Lords under one of the peer's lesser titles.
I'm unable to determine whether the writ qualifies them as a member of the peerage. In any case, the last time it was used was in 1992, when the aforementioned Robert Gascoyne-Cecil was accelerated to the House of Lords as Baron Cecil.
Side note, the businessman Robert Renwick was created Baron Renwick, of Coombe in the County of Surrey, on 23 December 1964. He had previously succeeded his father to the title of Baronet Renwick back in 1932. Though of course, baronetcies are not part of the peerage.